# How old is a mammoth's tusk if 25 percent of the original C-14 remains in the sample, if the half-life of C-14 is 5730 years?

Apr 10, 2016

The tusk would be 11 460 years old.

#### Explanation:

You calculate the number of half-lives and multiply by the length of one half-life.

The number of half-lives is $n = \frac{t}{t} _ \left(\frac{1}{2}\right)$, so $t = n {t}_{\frac{1}{2}}$.

For each half-life, you divide the total amount of the isotope by 2, so

$\frac{\text{Amount remaining" = "original amount}}{2} ^ n$ or

$A = {A}_{0} / {2}^{n}$

You can rearrange this to

${A}_{0} / A = {2}^{n}$

If the original amount was 100 %, and 25 % of the nuclide remains undecayed, we have

$\frac{100}{25} = {2}^{n}$

$4 = {2}^{n}$

$n = 2$

$t = n {t}_{\frac{1}{2}} = \text{2 × 5730 yr" = "11 460 yr}$