A wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made?

Question

A wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

Answer 1

A = A₀e^rt, now if t = 5730 years then A = A₀/2; A₀/2 = A₀e^5730r, r = ln(1/2)/5730 = - 0.000121;

So, A = A₀e^{- 0.000121t;} and A = A₀/4; t = ln(1/4)/(- 0.000121) = 11457 years ago.