Question

carbon-14 has a half-life of approximately 5,700 years. a fossil shell contain 25% of the original amount of its carbon-14. approximately how many years ago was this shell part of a living oranism?

Answer 1

The half-life equation $m=m_{0} (\frac{1}{2})^n$ in which n is equal to the number of half-lives that have passed can be altered to solve for n.

$n = \frac{log(\frac{m}{m_{0}} )}{log(\frac{1}{2})}$

$\frac{log(\frac{.25}{1} )}{log(\frac{1}{2})} = 2$

Then, the number of half-lives that passed can be multiplied by the length of a half-life to find the total time.

2 * 5700 =  11400 yr