SOLUTION: The percentage P of radioactive carbon-14 remaining in a fossil after t years is given by P:100(1/2)^t/5700. Suppose a fossil contains 35% of the carbon-14 that the organism contai

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The percentage P of radioactive carbon-14 remaining in a fossil after t years is given by P:100(1/2)^t/5700. Suppose a fossil contains 35% of the carbon-14 that the organism contai      Log On


   

Question 619318: The percentage P of radioactive carbon-14 remaining in a fossil after t years is given by P:100(1/2)^t/5700. Suppose a fossil contains 35% of the carbon-14 that the organism contained when it was alive.Estimate the age of the fossil.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The percentage P of radioactive carbon-14 remaining in a fossil after t years is given by P:100(1/2)^t/5700.
Suppose a fossil contains 35% of the carbon-14 that the organism contained when it was alive.
Estimate the age of the fossil.
100*%281%2F2%29%5E%28t%2F5700%29 = 35
%281%2F2%29%5E%28t%2F5700%29 = 35%2F100
using decimals here
%28.5%29%5E%28t%2F5700%29 = .35
using natural logs
t%2F5700*ln(.5) = ln(.35)
t%2F5700 = ln%28.35%29%2Fln%28.5%29
using a calc
t%2F5700 = 1.51457
t = 1.51457 * 5700
t = 8.633 yrs
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Check this on your calc: enter 100*.5^(8633/5700); results 35.00