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

Answer:

The approximate age of the bone is approximately 11552 years.

Step-by-step explanation:

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

$\frac{y}{a} = e^{-0.00012\cdot t}$ (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 $\frac{y}{a} = 0.25$, then the approximate age of the bone is:

$t = -8333.333\cdot \ln \frac{y}{a}$

$t\approx 11552.453\,yr$

The approximate age of the bone is approximately 11552 years.