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?

Algebra ->  Customizable Word Problem Solvers  -> Age -> 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?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 242017: Carbon dating: The amount of carbon-14 present in animal bones after t years is given by P%28t%29=P%280%29e%5E%28-0.00012t%29, a bone has lost 18% of it's carbon-14, How old are the bones?
Answer by Edwin McCravy(20055) About Me  (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 P%28t%29=P%280%29e%5E%28-0.00012t%29, 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 P%280%29 when it was fresh, after t
years P%28t%29 is 82% of P%280%29 or P%28t%29=0.82P%280%29.
 So we substitute +0.82P%280%29+ for P%28t%29 in

P%28t%29=P%280%29e%5E%28-0.00012t%29

0.82P%280%29=P%280%29e%5E%28-0.00012t%29.

Divide both sides by P%280%29

0.82=e%5E%28-0.00012t%29

Take natural logs of both sides:

ln%280.82%29=-0.00012t

Divide both sides by -0.00012

%28ln%280.82%29%29%2F%28-0.00012%29=t

1653.757823=t

Answer: about 1650 years old.

Edwin