Question 848513
An artifact was found and tested for its carbon-14 content.
 If 83% 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 year)
:
The radioactive decay formula
A = Ao*2^(-t/h), where
A = Amt after t time
Ao = initial amt
t = time of decay
h = half-life of substance
:
Let 1 = initial amt
then
.83 = amt after t time
:
1*2^(-t/5730) = .83
using common logs
{{{-t/5730}}}log(2) = log(.83)
{{{-t/5730}}} = {{{log(.83)/log(2)}}}
{{{-t/5730}}} = -.2688
t = -5730 * -.2688
t = 1540.33 ~ 1500 yrs