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Answer :
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.
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