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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt;
 &lt;ul&gt;
  
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. 40 for air)&lt;/span&gt;&lt;/li&gt;
  
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
  
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
  
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
  
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
  
 &lt;/ul&gt;
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. 40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. 40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt;
 &lt;div&gt;
  &lt;ol&gt;
   
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
   
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
   
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
   
   &lt;li&gt;count the remainder&lt;/li&gt;
   
   &lt;li&gt;repeat &lt;/li&gt;
   
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
   
  &lt;/ol&gt;
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;
  &lt;ol&gt;
   
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
   
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
   
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
   
  &lt;/ol&gt;
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;
  &lt;ol&gt;
   
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
   
   
   &lt;ol&gt;
    
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
    
    &lt;li&gt;16,000 years?&lt;/li&gt;
    
    &lt;li&gt;32,000 years?&lt;/li&gt;
    
   &lt;/ol&gt;
   
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
   
   
   &lt;ol&gt;
    
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
    
    &lt;li&gt;120 years?&lt;/li&gt;
    
    &lt;li&gt;45 years?&lt;/li&gt;
    
   &lt;/ol&gt;
   
  &lt;/ol&gt;
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;
  &lt;ol&gt;
   
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
   
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
   
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
   
  &lt;/ol&gt;
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt;
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;
 &lt;div&gt;Exponential growth:&lt;/div&gt;
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt;
 &lt;div&gt;If decay is &lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. 40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Exponential growth:&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt;
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt;
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt;
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt;
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt;
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt;
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt;
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. 40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Exponential growth:&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt;
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt;
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt;
 &lt;div&gt;BASE: how much you start with&lt;/div&gt;
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;
 &lt;div&gt;Lab: &lt;/div&gt;
 &lt;div&gt;
  &lt;ol&gt;
   
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
   
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
   
   
   &lt;ol&gt;
    
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
    
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
    
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
    
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
    
   &lt;/ol&gt;
   
  &lt;/ol&gt;
  &lt;div&gt;&lt;span&gt;Examples: (numbers are grossly estimated for comparison)&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt;
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (granite, hornblende)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Exponential growth:&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Lab: &lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;span&gt;Examples: (numbers are grossly estimated for comparison)&lt;/span&gt;&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (e.g. granite)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Exponential growth:&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Lab: &lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;span&gt;Examples: (numbers are grossly estimated for comparison)&lt;/span&gt;&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (e.g. granite)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;4 types of radiation:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Exponential growth:&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;Lab: &lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;span&gt;Examples: (numbers are grossly estimated for comparison)&lt;/span&gt;&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (e.g. granite)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;4 types of radiation:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Questions:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Problems:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;Setup for each problem:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential growth:&lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential Growth Lab: &lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Examples&lt;/b&gt;: (numbers are grossly estimated for comparison)&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (e.g. granite)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;4 types of radiation:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Questions&lt;/b&gt;:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Problems&lt;/b&gt;:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 8000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 8000 years?&lt;/li&gt;
     
    &lt;li&gt;16,000 years?&lt;/li&gt;
     
    &lt;li&gt;32,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Setup for each problem:&lt;/b&gt;&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential growth:&lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential Growth Lab: &lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Examples&lt;/b&gt;: (numbers are grossly estimated for comparison)&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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&lt;div class="wiki_entry"&gt;&lt;b&gt;Radon:&lt;/b&gt;&lt;/div&gt;
&lt;div class="wiki_entry"&gt; 
 &lt;ul&gt;
   
  &lt;li&gt;&lt;span&gt;Heavy (222 vs. ~40 for air)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;#2 cause of lung cancer in the us&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;emitted from radioactive rocks (e.g. granite)&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;in cigarette smoke&lt;/span&gt;&lt;/li&gt;
   
  &lt;li&gt;&lt;span&gt;alpha emitter (see below)&lt;/span&gt;&lt;/li&gt;
   
 &lt;/ul&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;4 types of radiation:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;beta: fast electron e- (charged, small)-stopped by foil&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;gamma: high energy photon, like light-stopped by lead&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Review Isotopes:&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Radon is 222/86: how many n, p and e?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many for C 14/6?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;b&gt;Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria&lt;/b&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Decay formula: At = Ao (0.5)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Growth formula: &lt;/span&gt;&lt;span&gt;At = Ao (2)^n&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;At = amount some time later, time t&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Ao = starting amount&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;n = number of half lives (t1/2) or doubling times (t2)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;We'll use M&amp;amp;Ms as our &amp;quot;atoms&amp;quot; for this:&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;pour out 32 M&amp;amp;Ms on a plate&lt;/li&gt;
    
   &lt;li&gt;drop into a shaker, shake, pour out on the plate&lt;/li&gt;
    
   &lt;li&gt;remove the ones with the M&amp;amp;M label facing up&lt;/li&gt;
    
   &lt;li&gt;count the remainder&lt;/li&gt;
    
   &lt;li&gt;repeat &lt;/li&gt;
    
   &lt;li&gt;graph number of M&amp;amp;Ms (y) number of turns (x)&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Questions&lt;/b&gt;:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;Does the number ever really get to zero in real live atoms?&lt;/li&gt;
    
   &lt;li&gt;What is the change in atoms at each turn?&lt;/li&gt;
    
   &lt;li&gt;How is this related to the amount of atoms left?&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Problems&lt;/b&gt;:&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;64 grams of C14/6 with half life of about 5000 years decays.&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;How much is left after 5000 years?&lt;/li&gt;
     
    &lt;li&gt;15,000 years?&lt;/li&gt;
     
    &lt;li&gt;30,000 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
   &lt;li&gt;Sr90/38 has a half life of about 30 years. If Ao is 200 grams,&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;how much is left after 60 years?&lt;/li&gt;
     
    &lt;li&gt;120 years?&lt;/li&gt;
     
    &lt;li&gt;45 years?&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Setup for each problem:&lt;/b&gt;&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;find n (60/30 = 2)&lt;/li&gt;
    
   &lt;li&gt;find Ao (200 grams)&lt;/li&gt;
    
   &lt;li&gt;At = 200(0.5)^2 = 50 grams&lt;/li&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;n.b. 45 grams is not a whole number of half lives&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;so what? just use the number to get 70 grams (try this)&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential growth:&lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt;Same deal as with decay, only we use 2 instead of 0.5&lt;/div&gt; 
 &lt;div&gt; 
  &lt;div&gt;Decay formula: At = Ao (0.5)^n&lt;/div&gt; 
  &lt;div&gt;Growth formula: At = Ao (2)^n&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;n is called t2 or the doubling time (you may have seen this in AP bio)&lt;/div&gt; 
 &lt;div&gt;Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?&lt;/div&gt; 
 &lt;div&gt;24/6 = 4 = n&lt;/div&gt; 
 &lt;div&gt;At = 1000(2)^4 = 16,000 bacteria&lt;/div&gt; 
 &lt;div&gt;This works for people, viruses, rhinos, even capybaras...&lt;/div&gt; 
 &lt;div&gt;One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;n.b. this depends on two things:&lt;/div&gt; 
 &lt;div&gt;RATE: the reproductive or decay rate&lt;/div&gt; 
 &lt;div&gt;BASE: how much you start with&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;b&gt;Exponential Growth Lab: &lt;/b&gt;&lt;/div&gt; 
 &lt;div&gt; 
  &lt;ol&gt;
    
   &lt;li&gt;&lt;span&gt;Start with 4 M&amp;amp;Ms, double until 32, graph&lt;/span&gt;&lt;/li&gt;
    
   &lt;li&gt;&lt;span&gt;On the same graph, repeat starting with 8 M&amp;amp;Ms&lt;/span&gt;&lt;/li&gt;
    
   
   &lt;ol&gt;
     
    &lt;li&gt;&lt;span&gt;What is the change in M&amp;amp;Ms at each turn?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;which graph has the steeper slope?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;how would birth control change t2?&lt;/span&gt;&lt;/li&gt;
     
    &lt;li&gt;&lt;span&gt;why did China have a one child policy had between 1980 and 2015?&lt;/span&gt;&lt;/li&gt;
     
   &lt;/ol&gt;
    
  &lt;/ol&gt; 
  &lt;div&gt;&lt;b&gt;Examples&lt;/b&gt;: (numbers are grossly estimated for comparison)&lt;/div&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Each country starts with about 30 million in this example:&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;How many in each case after 42 years?&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Canada t2=21 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Nigeria t2=7 years&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Japan t2 = -7 years (?)&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Rule of 70&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Countries use growth rate instead of t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;If growth rate is 7%, then 70/7 means 10 years is t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 14% then 70/14 means 5 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;if growth rate is 3.5% then 70/3.5 means 20 years for t2&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;&lt;br class="" /&gt;&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;span&gt;Populations depends on BASE and RATE&lt;/span&gt;&lt;/div&gt; 
 &lt;div&gt;&lt;br class="" /&gt;&lt;/div&gt;&lt;/div&gt;</string>
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	<string>Radioactivity-exponential decay and growth</string>
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