The half-life of carbon-14 is 5600 years. if a piece of charcoal made from the wood of a tree shows only 62 % of the carbon-14 expected in living matter, when did the tree die?

The amount of carbon-14 present obeys an exponential decay law.

A (t) = A (0) e-^kt

Get k from the half-life:

0.5 = 1e-^k (5600)

k = ln (0.5) / (-5600 years) = 1.2378 x 10^-4 years^-1

If only 73% of the carbon-14 remains after time T, then

0.73 = 1e^-kT

T = ln (0.73) / (-1.2378 x 10^-4 years^-1) = 2542.5 years

The tree has been dead for about 2542.5 years.