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Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation?

A) an = 18250n − 750
B) an = 750n + 18250
C) an = 18250n + 750
D) an = −750n + 18250

User Bmcculley
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1 Answer

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Final answer:

The correct equation that represents the situation of a car bought for $17,500 and losing $750 in value each year is an = -750n + 17500, which corresponds to option D, with a corrected initial value from the provided options.

Step-by-step explanation:

Jack bought a car for $17,500, and it loses $750 in value each year. To represent the value of the car after n years, we need an equation that incorporates the initial value and the annual depreciation. The value of the car after n years (an) can be calculated by subtracting the cumulative depreciation from the initial cost. The cumulative depreciation after n years is $750 times n, and when subtracted from the initial value of the car, the equation should look like this: an = -750n + 17500.

The equation matches with option D, which is formulated correctly as an = -750n + 18250.

To clarify, each year the value of the car decreases by $750, hence the negative sign before the 750. The initial value of the car is added as a constant which, in this case, is incorrect in the equation presented as an option due to the incorrect value. However, with the correct initial value of $17,500, the correct equation is an = -750n + 17500, which accounts for the depreciation over n years.

User Letfar
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