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:

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:

[tex]\frac{y}{a} = e^{-0.00012\cdot t}[/tex] (1)

Where:

[tex]y[/tex] - Current amount of carbon-14, no unit.

[tex]a[/tex] - Initial amount of carbon-14, no unit.

[tex]t[/tex] - Time, in years.

If we know that [tex]\frac{y}{a} = 0.25[/tex], then the approximate age of the bone is:

[tex]t = -8333.333\cdot \ln \frac{y}{a}[/tex]

[tex]t\approx 11552.453\,yr[/tex]

The approximate age of the bone is approximately 11552 years.

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