Question

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?

Answer 1

do you know what half-life means?

Answer 2

http://en.wikipedia.org/wiki/Half-life
Half-life (t1⁄2) is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period. While the term "half-life" can be used to describe any quantity which follows an exponential decay, it is most often used within the context of nuclear physics and nuclear chemistry—that is, the time required, probabilistically, for half of the unstable, radioactive atoms in a sample to undergo radioactive decay.

Answer 3

This problem you can solved at least in two different ways. One is an intuitive and the other you have to use two equations from the kinetic of a first order reaction.
The intuitive is just thinking that after the first half life (5720 years) you will have 50% converted of the carbon-14, in a second half-life time (2 x 5720 years) you will have converter an 50% of the 50%, that means a extra 25% that add to the first 50% converted in the first-half life make a total of 75% converted of the original carbon-14. That is what your sample has.
You can apply this approach always when you have a remain of 1/2,1/4,1/8,1/16,1/32 of the original amount that correlate with 1,2,3,4,5 half life respectively.

The mathematical approach is calculate the k of the reaction with the
t1/2= 0.69/k
and then the integrated rate law to calculate the time
\[\ \ln{[A]} = -kt + \ln{[A]_0}\]