Algebra I

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Please show me how to solve:

The value of a $20,000 car decreases every year, t. The equation below models this situation:

20000(1-0.04t)=13,000.

After how many years will the car be worth $13,000. Round to the nearest tenth if necessary.

  • Algebra I -

    Your equation is incorrect, it should say

    13000 = 20000(1-.04)^t
    then
    (.96)^t = .65
    take log of both sides
    log .96^t = .65
    t (log .96) = log .65
    t = log .65/log .96 = 10.55

    so it would take about 10.55 years or
    10.6 to the nearest tenth.

    check:
    .96(20000) = 19200
    .96(19200) = 18432.00
    .96(18432) = 17694.72
    etc
    (you will be able to do this 10 times and have a result of 13296.65
    doing it one more results in 12764.79

    My answer is reasonable.

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