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

VerifiedStep 1

1 of 2The amount present after $(t)$ years is given by the following equation:

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

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

$A(2580) = A_0\times 2^\frac{2580}{5730}$

Cancel common factor 10 as follows:

$A(2580) = A_0\times 2^\frac{258}{573}$

Use the calculator

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

Therefore the carbon still present $2580$ years after death is about $1.37A_0$ where $A_0$ is the original amount present.

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