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------------------------------------------------ Alice purchased a car for $24,000. The value of the car depreciates at a rate of 5.5% each year.

Which function equation represents the value of the car after $ t $ years?

A. $ f(t) = 24,000(0.055)^t $

B. $ f(t) = 24,000(1.055)^t $

C. $ f(t) = 24,000(5.5)^t $

D. $ f(t) = 24,000(0.945)^t $

Question

High School

Answer :

asarwar asarwar · Answer 1 · 2024-01-24T09:51:25-05:00

The function equation that represents the value of the car after t years is f(t) = 24,000(0.945)^t.

Option D is correct.

To find the function equation that represents the value of the car after t years, we need to consider the rate of depreciation.

Given:

- The car was purchased for $24,000.

- The value of the car depreciates at a rate of 5.5% each year.

The depreciation rate of 5.5% means that the car's value decreases by 5.5% each year.

The formula for the value of the car after t years can be expressed as:

Value of the car after t years = Initial value × (1 - Depreciation rate)^t

Substituting the given values:

f(t) = 24,000 × (1 - 0.055)^t

f(t) = 24,000 × (0.945)^t

Therefore, the function equation that represents the value of the car after t years is f(t) = 24,000(0.945)^t.

The correct answer is option D.