An archaeologist finds a pair of leather shoes that contain about 73.5% of the original conentration of carbon14. What is the approximate age of these shoes?

Answer 1

The half-life of Carbon-14 is 5730 years. So:

(1/2)^t/5730 = 0.735

Since 1/2 = 2^-1:

2^-t/5730 = 0.735

-t/5730 = log₂(0.735)

t = -5730·log₂(0.735)

Use your calculator to get the answer.