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30 December, 22:26

A new car sells for $30,000. The value of the car decreases by 16% annually. After how many years will the car be worth less than $10,000.

a. after 2 years

b. after 6 years

c. after 8 years

d. not enough information

(answer c is incorrect)

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Answers (1)
  1. 30 December, 22:53
    0
    Answer: after 6 years.

    Step-by-step explanation:

    We would apply the formula for exponential decay which is expressed as

    A = P (1 - r) ^t

    Where

    A represents the value of the car after t years.

    t represents the number of years.

    P represents the initial value of the car.

    r represents rate at which the value is decreasing.

    From the information given,

    P = 3000

    A = < 10000

    r = 16% = 16/100 = 0.16

    Therefore

    10000 = 30000 (1 - 0.16) ^ t

    1000/30000 = (0.84) ^t

    0.333 = (0.84) ^t

    Taking log of both sides to base 10

    Log 0.333 = log0.84^t = tlog0.84

    - 0.4772 = t * - 0.0757

    t = - 0.4772 / - 0.0757 = 6.3 years
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