Carbon-14 dating assumes that the carbon dioxide on Earth today has the same rad
ID: 2839398 • 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 = A0 * e^(-kt)
k = ln(2) / half-life
k = 0.0001213
A = A0 * e^(-0.0001212t)
Since the amount present now is 15% of original, we get :
0.15 * A0 = A0 * e^(-0.0001213t)
0.15 = e^(-0.0001213t)
ln(0.15) = -0.0001213t
t = ln(0.15) / -0.0001213
t = 15640 years