Question

A student in Greece discovers a pottery bowl that contains 28% of its original amount of C-14 find the age of the pottery bowl to the nearest year

Answer 1

The age of the pottery bowl is 10523 years.

Explanation:

Amount of substance:

The amount of a substance after t years is given by the following equation:

`A(t) = A(0)(1-r)^t`

In which A(0) is the initial amount and r is the decay rate.

Half-life of C14.

Researching, the half-life of c-14 is 5730 years.

This means that:

`A(5730) = 0.5A(0)`

We use this to find r. So

`A(t) = A(0)(1-r)^t`

`0.5A(0) = A(0)(1-r)^(5730)`

`(1-r)^(5730) = 0.5`

`\sqrt[5730]{(1-r)^(5730)} = \sqrt[5730]{0.5}`

`1 - r = 0.5^{(1)/(5730)}`

`1 - r = 0.99987903922`

So

`A(t) = A(0)(0.99987903922)^t`

Age of the pottery bowl:

We have that:

`A(t) = 0.28A(0)`

We have to find t. So

`A(t) = A(0)(0.99987903922)^t`

`0.28A(0) = A(0)(0.99987903922)^t`

`(0.99987903922)^t = 0.28`

`\log{(0.99987903922)^t} = \log{0.28}`

`t\log{0.99987903922} = \log{0.28}`

`t = \frac{\log{0.28}}{\log{0.99987903922}}`

`t = 10523.1`

So

The age of the pottery bowl is 10523 years.