Question

3. The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 70.3​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

10,071 years

Explanation:

If 'a' is the fraction remaining, it satisfies the equation ...

a = (1/2)^(t/5750)

Solving for t, we get ...

log(a) = log(1/2)×t/5750

t = 5750×log(a)/log(1/2) ≈ -19,101.09×log(a) . . . years

__

If 70.3% is lost, then 1 -0.703 = 0.297 is the fraction remaining. The age is estimated to be ...

-19,101.09×log(0.297) ≈ 10,071 . . . years

The bones were about 10,071 years old.