Radiocarbon dating

Question

A support pole for an ancient structure is found to have one-seventh of the carbon-14 of a modern, living tree. How long ago did the tree used to make the support pole die? Give your answer to the nearest whole number. 

Answer 1

Fraction remaining = 0.5ⁿ

n = number of half lives that have elapsed. To determine this, one needs to know the half life of carbon-14. It is 5730 years. We are given the fraction remaining (1/7), so we can calculate n (number of half lives elapsed).

1/7 = 0.142857 = 0.5ⁿ

Taking log of both sides: -0.845098 = n log 0.5 = --0.301n

n = -0.845098/-0.301

n = 2.81 half lives have elapsed

How many years is that?

2.81 half lives x 5730 yrs/half live = 16,101 years