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17 April, 10:52

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. 17 April, 12:26
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    The half-life of a radioactive material can be calculated by the expression:

    An = Ao e^-kt

    From the half-life data, we calculate the value of k.

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

    k = 0.0165

    For the second conditions, we can calculate the amount remaining after 8 days.

    An = 49 e^-0.0165 (8)

    An = 42.9395 kg
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