Question

you have decided to buy a new car, but you are concerned about the value of the car depreciating over time. you do some research on the model you are looking at and obtain the following information: suggested retail price - $18,790 depreciation per year - $1385 (it is assumed that this value is constant.) the following table represents the value of the car after n years of ownership. |n, years|v, value in dollars| |---|---| |0|18,790| |1|17,405| |2|16,020| |3|14,635| |5|11,865| |8|7710| determine the n-intercept of the graph of the car value equation v = -1385n + 18,790. what is the practical significance of the n-intercept? be sure to include units. a. the car is worth $1385 after 14 years. b. after 14 years, the car is worth $0.

Explanation:

Step1: Recall n - intercept definition

The n - intercept of a linear equation \(V=- 1385n + 18790\) is the value of \(n\) when \(V = 0\).

Step2: Solve for n when V = 0

Set \(V=0\) in the equation \(0=-1385n + 18790\).
Add \(1385n\) to both sides: \(1385n=18790\).
Divide both sides by 1385: \(n=\frac{18790}{1385}=13.567\approx14\) (rounded to a reasonable number of years).
This means when \(n\approx14\) years, the value of the car \(V = 0\) dollars. So the practical significance is that after about 14 years, the car is worth $0.

Answer:

b. After 14 years, the car is worth $0.