A Scientist determined that the bones from a mastodon had lo

A Scientist determined that the bones from a mastodon had lost 70.2% of their carbon-14. How old were the bones at the time they were discovered?

Solution

It is [ln(.298)/-0.693]*5730 = 1.747*5730 = 10010.2 years

-0.693 is ln (1/2), the half life, or 50%. If 75% were lost, that would be 2 half-lives or 11460 years, so this is in the range.

Determine the number of half life (1/2)^n=0.298
ln of both sides is n ln(1/2)=ln 0.298. Divide both sides by ln (1/2), which is -0.693