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?
The tree died about
? years ago
(Do not round until the final answer. Then round to the nearest whole number.)

The tree died about 3357 years ago.

Explanation:

The half life of carbon - 14 is given by

where

Substituting these values in the above equation, we get,

Taking In on both sides of the equation, we get,

Since, only 66% of Carbon - 14 remains after the time T.

Thus, we have,

Taking In on both sides of the equation, we get,

Thus, the tree died about 3357 years ago.