half life, died about x years ago

Question

the half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 7373?% of the? carbon-14 expected in living? matter, when did the tree? die? 

Answer 1

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.