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18 June, 18:59

A new car is purchased for 16000 dollars. The value of the car depreciates at 13.75% per year. To the nearest tenth of a year, how long will it be until the value of the car is 2900 dollars

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  1. 18 June, 21:59
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    It will take 11.5 years

    Step-by-step explanation:

    In this question, we are concerned with calculating the amount of time it will take for the value of a new car to depreciate to a certain amount, given the price it was bought and the percentage of yearly depreciation.

    To calculate this time, we need the appropriate exponential equation

    Mathematically, that could be expressed as;

    V = I (1-r) ^t

    where V is the future car value which is $2,900

    I is the initial car value which is $16,000

    r is the rate of depreciation which is 13.75% which is same as 13.75/100 = 0.1375

    and t is the time we want to calculate.

    Thus, plugging the values, we have;

    2900 = 16000 (1-0.1375) ^t

    divide through by 16,000

    0.18125 = 0.8625^t

    Finding the log of both sides, we have

    log 0.18125 = log0.8625^t

    log 0.18125 = t log 0.8625

    t = log 0.18125/log 0.8625

    t = 11.546

    To the nearest tenth of a year, t = 11.5 years
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