Carbon-14 is used to determine the time an organism was living. The amount of carbon-14 an organism has is constant with the atmosphere, but when an organism dies the carbon-14 decays at a half-life of 5,730 years. If an archeologist measured the amount of carbon-14 in an organism and it was 25% of the total amount of atmospheric C-14, what is the age of the organism? 1432.5 years 5,730 years 11,460 years 17,190 years

The age of the organism is approximately 11460 years.

Explanation:

The amount of carbon-14 decays exponentially in time and is defined by the following equation:

(1)

Where:

- Initial amount of carbon-14.

- Current amount of carbon-14.

- Time, measured in years.

- Time constant, measured in years.

Then, we clear the time within the formula:

(2)

In addition, time constant can be calculated by means of half-life of carbon-14 (), measured in years:

If we know that and , then the age of the organism is:

The age of the organism is approximately 11460 years.

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