Advanced Functions

he value of a new car depreciates at a rate of 12% per year.

Write an equation to represent the approximate value of a car purchased for $23 000.

Determine the value of the car two years after it is purchased.

Approximately how many years will it take until the car is worth $2300?

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  1. 1. V= C - rtC,
    Eq: V = C(1 - rt).

    V = value.
    C = cost.
    r = rate expresed as a decimal.
    t = time in years.

    2. V = 23000(1 - 0.12*2),
    V = 23000 * 0.76 = 17480.

    3. V = 23000(1 - 0.12t) = 2300,
    23000(1 - 0.12t) = 2300,
    Divide both sides by 23000:
    1 - 0.12t = 0.1,
    -0.12t = 0.1 - 1 = -0.90,

    t = -0.90 / -0.12 = 7.5 yrs.

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  2. Correction:

    1. Eq: V = C(1-r)^t

    2. V = 23,000(1-0.12)^2 = $17,811.20

    3. V = 23,000(1-0.12)^t = 2300
    (0.88)^t = 0.1
    t*Log(0.88) = Log0.1
    t = Log 0.1/Log0.88 = 18 Years.

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