Question

MAKING BRAINLIEST!!! PLS HELP

Autumn 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: Autumn wants to purchase a car that would have the greatest value in 5 years. Will there be any significant difference in the value of either car after 5 years? Explain your answer, and show the value of each car after 5 years. (4 points)

Answer 1

Answer:

• See below

Step-by-step explanation:

We can observe the first sequence is arithmetic, with common difference:

• d = 20000 - 26000 = 26000 - 32000 = - 6000

The second sequence is geometric with common ratio:

• r = 23336.75/27455 = 27455/32300 = 0.85

Part A and B

Car 1

Linear function:

• f(x) = 32000 - 6000x

Car 2

Exponential function:

• f(x) = 32300*0.85ˣ

Part C

Find f(5) for each function and compare:

• f(5) = 32000 - 6000*5 = 2000
• f(5) = 32300*0.85⁵ = 14331.68

Car 2 will have greater value