SOLUTION: Carbon dating: The amount of carbon-14 present in animal bones after t years is given by {{{P(t)=P(0)e^(-0.00012t)}}}, a bone has lost 18% of it's carbon-14, How old are the bones?

Question 242017: Carbon dating: The amount of carbon-14 present in animal bones after t years is given by , a bone has lost 18% of it's carbon-14, How old are the bones?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Carbon dating: The amount of carbon-14 present in animal bones after t years is given by , a bone has lost 18% of it's carbon-14, How old are the bones?


If the bone has lost 18% of its carbon in t years, 
then 82% of it remains after t years.

Since the amount of carbon was  when it was fresh, after t
years  is 82% of  or .
 So we substitute  for  in



.

Divide both sides by 



Take natural logs of both sides:



Divide both sides by 





Answer: about 1650 years old.

Edwin

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