The value V of a Porsche 718 Cayman that is t years old can be modeled by V(t) = 420,000(0.965)t (a) What would be worth the car′s

Question

The value V of a Porsche 718 Cayman that is t years old can be modeled by V(t) = 420,000(0.965)t (a) What would be worth the car′s worth in 2 years? (b) In how many years will the car be worth $325,000?

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Parker 3 days 2021-09-13T08:44:24+00:00 1 Answer 0

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    2021-09-13T08:45:48+00:00

    Answer:

    A. V (2) = $ 391,114.50

    B. t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days  

    Step-by-step explanation:

    Given formula:

    V(t) = 420,000 * (0.965)^t

    A. What would be worth the car′s worth in 2 years?

    V(t) = 420,000 * (0.965)^t

    We replace t by 2, as follows:

    V(2) = 420,000 * (0.965)²

    V(2) = 420,000 * 0.931225

    V (2) = $ 391,114.50

    B. In how many years will the car be worth $325,000?

    V(t) = 420,000 * (0.965)^t

    We replace V(t) by 325,000, as follows:

    325,000 = 420,000 * (0.965)^t

    325,000/420,000 = (0.965)^t

    0.77381 =  (0.965)^t

    t = log 0.965(0.7738)  

    t = log 0.7738/log 0.965  

    t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days  

    0.2 years = 0.2 * 12 = 2.4 months

    0.4 months = 0.4 * 30 = 12 days

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