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14 May, 20:21

A car is sold for $22,000. After one year, the value of the car is $18,700. Write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.

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Answers (2)
  1. 14 May, 23:08
    0
    Y = 22000 - 3300x

    ...
  2. 14 May, 23:49
    0
    Step-by-step explanation:

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

    y = b (1 - r) ^x

    Where

    y represents the value of the car after x years.

    x represents the number of years.

    b represents the initial value of the car.

    r represents rate of decay.

    From the information given,

    A = $18700

    P = $22000

    x = 1

    Therefore,

    18700 = 22000 (1 - r) ^1

    18700/22000 = (1 - r) ^1

    0.85 = 1 - r

    r = 1 - 0.85

    r = 0.15

    Therefore, the exponential function is

    y = 22000 (1 - 0.15) ^x

    y = 22000 (0.85) ^x
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