Question

An anthropologist finds bone that her instruments measure it as 0.369% 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.

Answer 1

a/2=ar^5730

0.5=r^5730

0.5^(1/5730)=r

.00369=0.5^(t/5730)

ln(.00369)/ln(0.5)=t/5730

t=5730ln(.00369)/ln(0.5) years

t≈46310.8 years (to the nearest tenth of a year)