SOLUTION: 2.1. An anthropologist finds bone that her instruments measure it as 0.717% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 2.1. An anthropologist finds bone that her instruments measure it as 0.717% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did t      Log On


   

Question 1002738: 2.1. An anthropologist finds bone that her instruments measure it as 0.717% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
When person was alive, 1.000% of expected Carbon-14; today, found 0.717%.

C=Ie%5E%28-kt%29 decay model

ln%28C%29=ln%28Ie%5E%28-kt%29%29
ln%28C%29=ln%28I%29-kt%2Aln%28e%29
ln%28C%29=ln%28I%29-kt
ln%28C%29-ln%28I%29=-kt
kt=ln%28I%29-ln%28C%29
kt=ln%28I%2FC%29----------Use again later
k=ln%28I%2FC%29%2Ft
Substitute values to evaluate k using half-life
k=ln%281%2F%281%2F2%29%29%2F5730
k=ln%282%29%2F5730
highlight_green%28k=0.00012097%29


Model is now C=I%2Ae%5E%28-0.00012097t%29.

How old is the found bone?
from kt=ln%28I%2FC%29
t=ln%28I%2FC%29%2Fk
t=ln%281%2F0.717%29%2F0.00012097
highlight%28t=2750%2Ayears%29