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-1
4 expected in living matter, when did the tree die?
1 answer:
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.
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