Question

The bones were about ___ years old. Round to the nearest integer as needed.

Answer 1

Since they lost 69.1 %, only 30.9 % remains. The correct equation for the remaining amount is

`A(t)=A_0(0.5)^{(t)/(5750)}`

t = years since 100% was present, A0 = initial amount = 100% .

Get time T to drop to 30.9% from

`30.9=100(0.5)^{(T)/(5750)}`
`0.309=(0.5)^{(T)/(5750)}`

Take log both sides,

`\log 0.309=(T)/(5750)\log 0.5`
`-0.51004=(T)/(5750)(-0.30103)`
`1.694=(T)/(5750)`
`T=9742.3\text{ years}`

Hence the bones are 9742.3 years old when they are discovered.