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?

Following are the calculation when the tree dies:

Given:

Carbon-14 half-life = 5600 years

To find:

The tree dies in years=?

Solution:

Using formula:

Using natural log:

Therefore, the final answer is "3862 years".

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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.