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28 June, 21:24

A new car is purchased for 18500 dollars. The value of the car depreciates at 10.75%

per year. To the nearest year, how long will it be until the value of the car is 5000 dollars?

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  1. 28 June, 21:52
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    Answer: 11.5 years

    Step-by-step explanation:

    Hi, to answer this question we have to apply an exponential decay function:

    A = P (1 - r) ^ t

    Where:

    p = original value

    r = depreciation rate (decimal form) = 10.75 / 100 = 0.1075

    t = years

    A = value after t years

    Replacing with the values given:

    5000 = 18500 (1 - 0.1075) ^t

    Solving for t:

    5000/18500 = (1 - 0.1075) ^t

    0.27027027 = 0.8925 ^t

    ln 0.27027027 = ln 0.8925 ^t

    ln 0.27027027=t (ln 0.8925)

    ln 0.27027027 / ln 0.8925 = t

    11.5 years = t

    Feel free to ask for more if needed or if you did not understand something.
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