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11 November, 14:17

Brent purchased a used vehicle that depreciates under a straight-line method. The initial value of the car is $7500, and the salvage value is $500. If the car is expected to have a useful life of another 7 years, how much will it depreciate each year?

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  1. 11 November, 14:36
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    Let the value of the vehicle be described by the equation

    V = a + bx

    where x = number of years since purchase

    a, b are constants.

    When x = 0, V = $7500. Therefore

    a + b*0 = 7500

    a = 7500

    When x = 7, V = $500. Therefore

    7500 + 7b = 500

    7b = 500 - 7500 = - 7000

    b = - 7000/7 = - 1000

    The equation is

    V = 7500 - 1000x

    The slope of this equation is the depreciation rate, and it is - $1000 per year.

    Answer: $1000 depreciation per year.
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