Question

The amount of carbon-14 in an object is given by y = ae– 0.00012t where a is the initial amount of carbon and t is the age in years. A fossil bone contains 25% of its original carbon-14. What is the approximate age of the bone?

Answer 1

The approximate age of the bone is approximately 11552 years.

Explanation:

The current proportion of carbon-14 with respect to its original amount is defined by following formula:

`(y)/(a) = e^(-0.00012\cdot t)` (1)

Where:

`y` - Current amount of carbon-14, no unit.

`a` - Initial amount of carbon-14, no unit.

`t` - Time, in years.

If we know that
`(y)/(a) = 0.25`, then the approximate age of the bone is:

`t = -8333.333\cdot \ln (y)/(a)`

`t\approx 11552.453\,yr`

The approximate age of the bone is approximately 11552 years.