Belinda is thinking about buying a car for $18,500. 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) 17,390 16,346.60 15,365.80

Car 2 (value in dollars) 17,500 16,500 15,500

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.

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

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

Step-by-step explanation:

Part A

The function that can be used to describe the value of each of the cars after a fixed number of years is an exponential function. This is because the value is reducing at a constant rate (in percent) each year.

Part B

The formula for determining exponential decay is expressed as

A = P (r) ^t

Where

A represents the value after t years.

P represents the initial value.

r represents the rate of decay.

For Car 1,

r = 16346.6/17390

r = 0.94

The function describing the value after x years is

f (x) = 17390 (0.94) ^x

For Car 2,

r = 16500/17500

r = 0.943

The function describing the value after x years is

f (x) = 17500 (0.943) ^x

C)

If she buys Car 1 for $18500, after 9 years, the value will be.

f (x) = 18500 (0.94) ^9

f (x) = $10600

If she buys Car 2 for $18500, after 9 years, the value will be.

f (x) = 18500 (0.943) ^9

f (x) = $10909

The difference would be

10909 - 10600 = $309