Question

A wooden artifact is found in an ancient tomb. Its carbon-14 activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of carbon-14 was initially present in the wood from which the artifact was made, determine the age of the artifact.

Calculate how long it take for the decay rate to decrease to 60% of the initial value, when the half life is that of C-14, which is 5568 years. They expect you to look that up, or know it.

Let t = the age in years
2^(-t/5568) = 0.6
Solve for t.
(-t/5568)*log 2 = log 0.6
-t/5568 = log .6/log2 = -.737
t = 4100 years

Answer 1

Half life of C-14 is 5730 yrs. Which would give you 4.22x10^3 yrs as your answer.

Answer 2

9200 years