Write an exponential decay model for each situation. The value of x for each value of f(x) will lie between two consecutive whole numbers. L

Question

Write an exponential decay model for each situation. The value of x for each value of f(x) will lie between two consecutive whole numbers. List the whole numbers.

initial value: 1,800
decay rate: 7%
f(x) = 400

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Thanh Hà 3 years 2021-09-05T14:00:13+00:00 1 Answers 117 views 0

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  1. Nem
    0
    2021-09-05T14:01:56+00:00
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    Answer:

    The numbers are;

    20 and 21

    Step-by-step explanation:

    A general form of an exponential decay model can be presented as follows;

    f(x) = a·(1 + r)ˣ

    Where;

    f(x) = The output for a given input variable, ‘x’

    x = The input variable

    a = The initial value

    r = The growth (+ve) or decay (-ve) rate

    When f(x) = 400, a = 1,800, r  = -7% = -0.07, we get;

    400 = 1,800 × (1 – 0.07)ˣ

    (1 – 0.07)ˣ = 400/1,800 = 2/9

    ln((1 – 0.07)ˣ) = ln(2/9)

    x = ln(2/9)/(ln(1 – 0.07)) ≈ 20.73

    The value of ‘x’ lies between 20 and 21.

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