Question

Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.

Number of years
1
2
3
Car 1 (value in dollars)
18,500
17,390
16,346.60
Car 2 (value in dollars)
18,500
17,500
16,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Baxter wants to purchase a car that would have the greatest value in 10 years. Will there be any significant difference in the value of either car after 10 years? Explain your answer, and show the value of each car after 10 years.

Answer 1

For part A: one of the cars is decreasing at a constant dollar amount each time, while the other is decreasing at a constant ratio - can you figure out which is which?

For part B:

The linear function will be something like final value = initial value - (amount decrease per year)(# of years)

While the exponential function will look something like

final value = initial value * (1 - rate of decrease)^(# of years)

Plug in the appropriate values from the problem

For part C, plug in 10 years into both functions and see how much the difference is