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.