Carbon-14(14C) dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago. If this is true, then 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 similar tree today. A piece of ancient charcoal contains only 18% 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 your answer to the nearest integer.
A)2,310 years
B)33,123 years
C)2,315 years
D)14,139 years
E)14,144 years

Question

Quizplus · Accepted Answer

We know that the amount of 14C absorbed by the ancient charcoal is only 18% of the amount of 14C absorbed by modern charcoal, which means that the amount of 14C remaining in the ancient charcoal is 18% of what it was when the tree was alive. Let x be the number of years ago that the tree was burned to make the ancient charcoal. Then, we can use the fact that the half-life of 14C is 5715 years to write the equation:

0.18 = (1/2)^(x/5715)

Solving for x, we get:
x/5715 = log(0.18)/log(1/2) 
x = 14,139 (rounded to the nearest integer)

Therefore, the tree was burned approximately 14,139 years ago. The answer is D.

Carbon-14(14C) Dating Assumes That the Carbon on the Earth Today