An artifact was found and tested for its carbon-14 content. If 70% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

Answer 1

Use
amount = c (1/2)^(t/k), where k is the half-life period
so ....

.7 = 1(1/2)^(t/5730)
.7 = (2)^(-t/5730)
ln .7 = ln ( 2^(-t/5730) )
ln .7 = -t/5730 (ln2)
-t/5730 = ln .7/ln 2 = -.514573...
t = 2948.5 years
or 2900 to the nearest 100 years