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18 August, 18:28

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. Write an exponential function for the graph.

b. Use the function in part a to find the value of the boat after 9.5 years.

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  1. 18 August, 18:54
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    For the answer to the question above,

    V (n) = a * b^n, where V (n) shows the value of boat after n years.

    V (0) = 3500

    V (2) = 2000

    n = 0

    V (0) = a * b^0 = 3500

    a = 3500

    V (2) = a * b^2

    2000 = 3500 * b^2

    b = sqrt (2000/3500)

    b ≈ 0.76

    V (n) = 3500 * 0.76^n

    We can check it for n = 1 which is close to 2500 in the graph:

    V (1) = 3500 * (0.76) ^1

    V (1) = 2660

    And in the graph we have V (3) ≈ 1500,

    V (n) = 3500 * (0.76) ^3 ≈ 1536

    Now n = 9.5

    V (9.5) = 3500 * (0.76) ^ (9.5)

    V (9.5) ≈ 258
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