The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 64.8% of their carbon-14

Question

The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 64.8% of their carbon-14. How old were the bones at the time they were discovered?

Answer 1

Since they lost 64.8%, only 35.2% remains. The correct equation for the remaining amount is

A(t) = A₀ (0.5)^t/5750

t = tears since 100% was present

A₀ = initial amount = 100%

A(t) = 100 (0.5)^t/5750

Get time T to drop to 35.2% from

35.2 = 100 (0.5)^T/5750

0.352 = (0.5)^T/5750

log0.352 = (T/5750) log0.5

T = 5750 (log0.352 / log0.5) years = 8661.5 years

Note it does not matter what base you use for the logs, as long as it is the same for both.