The selling price of a car is 12,500. Each year, it loses 10% of its value. Find the exponential function that gives the value of the car t years after it's purchase. Write your answer in the form f (t) = a (b) ^t

Question

Mathematics

Thalia Crosby

29 March, 03:22

The selling price of a car is 12,500. Each year, it loses 10% of its value. Find the exponential function that gives the value of the car t years after it's purchase. Write your answer in the form f (t) = a (b) ^t

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Answers (1)

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Gilda · Answer 1

f (t) = 12,500 (0.9) ^t

Step-by-step explanation:

So we start with the base value of 12,500, which will be "a" in the formula f (t) = a (b) ^t.

to find "b" we use the percentage. b will be 1 + the percentage for an increasing value, or 1 - the percentage if it is a decrease. This is decreasing by 10%, which is 0.10 in decimal form. so 1 -.10 which is 0.90 which is b.

so,

f (t) = 12,500 (0.9) ^t