The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of mil

Question

The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of milligrams of the substance and t represents the time. In years. In the function p(t), explain what 0.25 and 500 represent.​

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Hải Đăng 3 years 2021-09-05T14:21:43+00:00 1 Answers 35 views 0

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  1. thanhcong
    0
    2021-09-05T14:23:20+00:00
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    Given:

    The function is:

    p(t)=500(0.25)^t

    Where p(t) represents the number of milligrams of the substance and t represents the time.

    To find:

    The correct explanation for the number 0.25 and 500 in the given function.

    Solution:

    The general exponential function is:

    y=ab^x           …(i)

    Where, a is the initial value and b is the growth/decay factor. If 0<b<1, then decay factor and if b>1, then growth factor.

    We have,

    p(t)=500(0.25)^t           …(ii)

    On comparing (i) and (ii), we get

    a=500, it means initial there are 500 milligrams of the substance.

    b=0.25, this value is less than 1, it means the substance is decreasing by a factor of 0.25.

    Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.

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