WILL MARK BRAINLIEST AND GIVE 75 POINTS!!!

Summer is thinking about buying a car for $45,000. 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) 40,500 36,450 32,805
Car 2 (value in dollars) 42,000 39,000 36,000

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: Summer wants to purchase a car that would have the greatest value in 13 years. Will there be any significant difference in the value of either car after 13 years? Explain your answer, and show the value of each car after 13 years. (4 points)

The values for Car 1 have a common ratio of 40500/45000 = 0.9. An exponential function is used to describe a sequence where the terms have a common ratio.

The values for Car 2 have a common difference of 42000-45000 = -3000. A linear function is used to describe a sequence where the terms have a common difference.

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Part B

An exponential function can be written as ...

f(x) = (initial value)·(common ratio)^x

A linear function can be written as ...

f(x) = (common difference)x + (initial value)

The functions are ...

Car 1: f(x) = 45000·0.9^x

Car 2: f(x) = -3000x +45000

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Part C

The formulas for the different car values after 13 years give ...

Car 1: f(13) = 45000·0.9^13 ≈ 11,348

Car 2: f(13) = -3000(13) +45000 = 6,000

The value of Car 1 will be almost double the value of Car 2 after 13 years. Yes the difference in value is significant.