Question

Belinda is thinking about buying a car for $38,000. 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) 32,000 26,000 20,000
Car 2 (value in dollars) 32,300 27,455 23,336.75


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: Belinda wants to purchase a car that would have the greatest value in five years. Will there be any significant difference in the value of either car after five years? Explain your answer, and show the value of each car after five years. (4 points)

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Car A follows a linear pattern, as a straight well fitted line was obtained from the regression model, with a fixed amount as Depreciation per year.

CarB follows an exponential trve das obtained on the regression plot.

Using technology :

Where, f(x) = price of car

The linear function for car 1 :

f(x) = - 6000x + 38000

THE exponential function :

f(x) = 38000(0.85)^x

In 5 years :

Car 1:

f(5) = - 6000(5) + 38000 = 8000

Car 2 :

f(x) = 38000(0.85)^5 = 16,860.801

Hence, car 2 has the the greatest value after 5 years