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10 September, 01:22

A company paid $150 comma 000 for a new 18-wheeler. When it is 9 years old it will be worth $51 comma 000. Using straight-line depreciation, the value of the truck in dollars, V, is a linear function of its age in years, n. Find the function and the value when the truck is 8 years old

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  1. 10 September, 03:41
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    V = - 11,000n + $150,000; $62,000

    Explanation:

    Given that,

    Cost of new 18-wheeler = $150,000

    When it is 9 years old, worth = $51,000

    Let the function be: V = xn + y

    where,

    x and y are constants.

    V = value of the truck in dollars

    n = age in years

    When n = 0, V = $150,000

    When n = 9, V = $51,000

    According to the equation,

    When n = 0, V = $150,000

    $150,000 = x (0) + y

    $150,000 = y

    When n = 9, V = $51,000

    V = xn + y

    $51,000 = x (9) + $150,000

    $51,000 - $150,000 = 9x

    -$99,000 = 9x

    -$11,000 = x

    Function: V = - 11,000n + $150,000

    Therefore,

    When the truck is 8 years old, the value of truck is as follows:

    = xn + y

    = (-$11,000) (8) + $150,000

    = - $88,000 + $150,000

    = $62,000
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