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9 November, 05:11

3. The half-life of a certain radioactive material is 42 days. An initial amount of the material has a mass of 49

kg. Write an exponential function that models the decay of this material. Find how much radioactive material

remains after 8 days. Round your answer to the nearest thousandth

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  1. 9 November, 05:29
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    An exponential function that models a radioactive decay would be written as:

    An = Ao e^-kt

    where An is the amount of the material left after a certain time, t. Ao is the initial amount. k is a constant.

    We use the value of the half-life to find the value of k.

    1/2Ao = Ao e^-k (42 days)

    k = 0.0165

    The amount remaining after 8 days is calculated as follows:

    An = 49 e^ (-0.0165) (8)

    An = 42.9407 kg
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