Question

A minivan is purchased for $29,248. The value of the vehicle depreciates over time. Describe the advantages and disadvantages of using a linear function to represent the depreciation of the car over time. Describe the advantages and disadvantages of using an exponential function to represent the depreciation of the car over time. The minivan depreciates $3,000 in the first year. Write either a linear or exponential function to represent the value of the car x years after it was sold.

Answer 1

Advantage: If a car is losing value at a constant rate, then the linear function represents accurately the depreciation of the car.

Disadvantage: If the car is not losing value at a constante rate, then when we calculate the value of the car 'x' years after it was sold, we won't get an accurate result.

If the minivan is purchased for $29,248 and the first year it depreciates $3000. Then, the linear function that represents the value of the car is:

y = $29,248 - $3000x

Where 'y' represents the value of the car, and 'x' represents the number of years.

Let us explain this with an example. After 6 years, the price will be:

y = $29,248 - $3000(6) = $11,248