Homework question help

Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 81.5​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

Suppose the initial amount of carbon-14 was 1 unit. When the bones were found, there was 81.5% gone, so this is 100%- 81.5% = 18.5% or .185 units.

0.185 = 1*(1/2)^(t/5750) = (1/2)^(t/5750)

log _1/2 (0.185) = t/5750

t = log _1/2 (0.185) * 5750

t = [ log ₁₀ (0.185) / log ₁₀ (1/2) ] * 5750

t ≈ 13,997.816238575

t ≈ 13,998 years

Answer 2

0.185 = (0.5)^t/5750

ln 0.185 = (t/5750) ln 0.5

Can you solve for t and answer?