SOLUTION: An artifact was found and tested for its carbon-14 content. If 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has

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Question 940487: An artifact was found and tested for its carbon-14 content. If 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)

Answer by ankor@dixie-net.com(22740) (Show Source):
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An artifact was found and tested for its carbon-14 content.
If 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)?
(Carbon-14 has a half-life of 5,730 years.)
:
The radioactive decay formula: A = Ao(2^(-t/h)), where:
A = amt present after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
:
Let initial amt = 1, then A = .77
1(2^(-t/5730)) = .77
using natural logs
ln(2^(-t/5730)) = ln(.77)
log equiv of exponents
ln(2) = ln(.77)
=
use a calc
= -.377
multiply both sides by -5730
t = -5730 * -.377
t = +2160 ~ 2200 yrs