Question

Carbon 14 dating assumes that the carbon
dioxide on earth today has the same radioactive content as it did centuries ago. If this
is true, the amount of carbon 14 absorbed by
a tree that grew several centuries ago should
be the same as the amount of carbon 14 absorbed by a tree growing today. A piece of
ancient charcoal contains only 48% as much
radioactive carbon as a piece of modern charcoal.
How long ago was the tree burned to make
the ancient charcoal if the half-life of carbon
14 is 5730 years?
Answer in units of years

Answer 1

A piece of ancient charcoal contains only 15% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal if the half-life of Carbon 14 is 5715 years?
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A(t) = Ao(1/2)^(t/5715)
(0.15)Ao = Ao(1/2)^(t/5715)
0.15 = (1/2)^t/5715
Take the log of both sides to get:

log0.15 = (t/5715)log0.5
t/5715 = log0.15/log0.5
t = 5715(2.736965594...
t = 15641.76 years