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?
The tusk would be 11 460 years old.
You calculate the number of half-lives and multiply by the length of one half-life.
The number of half-lives is
For each half-life, you divide the total amount of the isotope by 2, so
You can rearrange this to
If the original amount was 100 %, and 25 % of the nuclide remains undecayed, we have