The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 66​% of the​ carbon-14 expected in living​ matter, when did the tree​ die?

Answer 1

There are several ways to approach this. One easy way is to use the relationship that the fraction remaining (66%) is equal to 0.5^n where n is the number of half lives that have elapsed. In this problem, we want to solve for n.

0.66 = 0.5^n

log 0.66 = n log 0.5

-0.1805 = -0.301n

n = 0.5997 half lives have elapsed

How much time is that?

0.5997 half lives x 5600 yrs/half life = 3358 years