Question

Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.

Car 1 (value in dollars)
Year 1: 18,500
Year 2: 17,390
Year 3: 16,346.60

Car 2 (value in dollars)
Year 1: 18,500
Year 2: 17,500
Year 3: 16,500

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: Baxter wants to purchase a car that would have the greatest value in 10 years. Will there be any significant difference in the value of either car after 10 years? Explain your answer, and show the value of each car after 10 years.

Answer 1

Car 1: It is an exponential function that is given as P = 18,500 (0.9595)ⁿ and the price after 10 years is $12,235.5.

Car 2: It is a linear function that is given as 2000x + 3y = 55500 and the price after 10 years is $11,833.33.

And Yes, there is a significant difference.

What is a function?

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.

Car 1 (value in dollars)

Year 1: 18,500

Year 2: 17,390

Year 3: 16,346.60

Car 2 (value in dollars)

Year 1: 18,500

Year 2: 17,500

Year 3: 16,500

The exponential function describes car 1.

Then the function will be

$\rm P = 18500\times (0.95995)^n$

The linear function describes car 2.

$\rm y \ - \ 18500 = \dfrac{-2000}{3}(x - 0)\\\\\\3y - 55500 = -2000x\\\\\\2000x +3y = 55500$

Then the value of the car 1 after 10 years will be

$\rm P = 18500\times (0.95995)^{10}\\\\\\P = \ \ 12,235.5$

Then the value of the car 2 after 10 years will be

$\rm 2000 \times 10 +3y = 55500\\\\y = \ \ 11,833.33$

Yes, there is a significant difference.

More about the function link is given below.

https://brainly.com/question/5245372

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