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?

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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