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27 July, 08:31

The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

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  1. 27 July, 12:09
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    F (t) = 361e^kt; where f (t) is the amount of radioactive material remaining after t days, k is the decay constant and t is the time elasped.

    180.5 = 361e^ (32k)

    e^ (32k) = 180.5/361 = 1/2

    32k = ln (1/2)

    k = ln (1/2) / 32

    The required exponential function is f (t) = 361e^ (((ln 1/2) / 32) t)

    After 5 days, f (5) = 361e^ (((ln 1/2) / 32) 5) = 323.945 kg.
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