math
posted by Anonymous on .
An artifact was found and tested for its carbon14 content. If 83% of the original carbon14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon14 has a halflife of 5,730 years.

x = Xo e^kt
(x/Xo) = 1/2 = e^(5730)k
ln .5 = 5730 k
.693 =5730 k
k = 1.21*10^4
then
.83 = e^1.21*10^4 t
ln .83 = 1.21 * 10^4 t = .186
t = 10^4 * .154 = 1540 or 1500 years old