The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the bones from a mastodon had lost 61.9% of their carbon 14 how old were the bones at the time they were

Question

The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the bones from a mastodon had lost 61.9% of their carbon 14 how old were the bones at the time they were discovered?

Answer 1

Fraction remaining = 0.5ⁿ where n = # of elapsed half lives

So we need to first find how many 1/2 lives have elapsed

Fraction remaining = 100 - 61.9 = 38.1% = 0.381 fraction

0.381 = 0.5ⁿ

log 0.381 = n log 0.5

n = 0.419/0.301 = 1.39 half lives

5750 yrs x 1.39 = 8004 years = age of bones.