Question

An anthropologist finds bone that her instruments measure it as 0.061% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?

Answer 1

The Carbon-14 dating formula is
$N(t)=N_{0}e^{-0.693t}$
where
N₀ = mass of C-14 at death
N(t) = mass of C-14 at t years after death

Given:
N(t)/N₀ = 0.061% = 6.1x10⁻⁴
Therefore
$e^{-0.693t}=6.1\times10^{-4}$
-0.693t = ln(6.1x10⁻⁴)
t = ln(6.1x10⁻⁴)/(-0.693) = 10.68

Answer: 10.68 years ago