Question

Autumn 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)
38,000
32,000
26,000
Car 2 (value in dollars)
38,000
32,300
27,455

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: Autumn wants to purchase a car that would have the greatest value in 6 years. Will there be any significant difference in the value of either car after 6 years? Explain your answer, and show the value of each car after 6 years. (4 points)

(10 points) ALGEBRA 1 only

Answer 1

Part A

Car 1

• 26000 - 32000 = 32000 - 38000 = -6000
• Since the difference is common this is a linear function

Car 2

• 32300/38000 = 27465/32300 = 0.85
• Since the ratio is common this is an exponential function

Part B

Car 1

• V(x) = 38000 - 6000x

Car 2

• V(x) = 38000*0.85ˣ

Part C

Find V(6) for both cars and compare

Car 1

• V(6) = 38000 - 6*6000 = 2000

Car 2

• V(6) = 38000*0.85⁶ = 14331.68

As we see the difference is significant and car 2 has much greater value