Question

Living organisms contain a certain amount of carbon-14. After death, this amount decays according to the equation in Exercise69 (this is used in carbon-14 dating). What percentage of an organism's carbon- 14 is still present 2580 years after death?

Solution

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The amount present after (t)(t) years is given by the following equation:

A(t)=A0 2t5730A(t) = A_0 \ 2^\frac{t}{5730}

If A0=55.0A_0=55.0 mg,\ then the carbon is present after t=2580t=2580 years. Then

A(2580)=A0×225805730A(2580) = A_0\times 2^\frac{2580}{5730}

Cancel common factor 10 as follows:

A(2580)=A0×2258573A(2580) = A_0\times 2^\frac{258}{573}

Use the calculator

A(2580)=1.37A0 mgA(2580) =1.37A_0\text{ mg}

Therefore the carbon still present 25802580 years after death is about 1.37A01.37A_0 where A0A_0 is the original amount present.

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