Question

The amount of​ carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27​% of its​ carbon-14. How old are the​ paintings?

Answer 1

The painting is
`t = 10911.1 \ years \ old`

Explanation:

From the question we are told that

The amount of carbon present after t year is

`y(t) = y_o * e ^(-0.00012t)` {Note ; This is the function }

Here
`y(t)` is the amount of carbon-14 after time t

`y_o` the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

Then it mean that

`y(t) = 0.27 y_o`

So the equation is represented as

`0.27 y_o = y_o * e ^(-0.00012t)`

=>
`0.27 = * e ^(-0.00012t)`

=>
`ln(0.27) = -0.00012t`

=>
`- 1.30933 = -0.00012t`

=>
`t = (-1.30933)/(-0.00012)`

=>
`t = 10911.1 \ years`