Carbon-14 dating assumes that the carbon dioxide on Earth today has the same rad
ID: 2839469 • Letter: C
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 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a tree growing today. A piece of ancient charcoal contains only 15% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of 14C is 5715 years. Round to the nearest year.)
Explanation / Answer
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