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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?

User SQiShER
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1 Answer

4 votes

Answer:

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.

User ComputerGuyCJ
by
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