Half-life, finding time?

The half-life of carbon 14 is 5730 years. Human hair from a grave in Africa proved to have only 51% of the carbon 14 living tissue. When was the body buried?

Half-life, finding time?

The its age is really close to 5730 years since almost 1/2 of the Carbon 14 remains. The percentage left P = (1/2)^(T/H) where T is the time that has passed, and H is the half-life in years. We know H is 5730 years, the current percentage left is 51% (0.51), and we want to find T.

0.51 = 0.5^(T/5730)

logbase0.5 0.51 = T/5730

T = 5730 logbase0.5(0.51)

log base 0.5 of 0.51 = ln(0.51) / ln(0.5) or 0.971431

So T = 0.971431 x 5730 or 5,566 years ago