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30 January, 10:24

A radioactive substance decays by x % each day. After 8 days half of the substance has decayed. Find the value of x. Give your answer to 1 decimal place.

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  1. 30 January, 10:31
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    8.3

    Step-by-step explanation:

    Let Ao be the original amount and A the amount after t days.

    Then we have the exponential function

    A = Ao (1 - x) ^t or

    A/Ao = (1 - x) ^t

    When t = 8, A/Ao = 0.5

    0.5 = (1 - x) ^8

    (0.5) ^ (1/8) = 1 - x

    0.917 = 1 - x

    x = 1 - 0.917 = 0.083 = 8.3 %

    The substance decays by 8.3 % each day.
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