Question

the following table shows the mileage on and corresponding value of a used 2004 mini cooper, 2 - door hatchback one year after it was purchased.
mileage 10,000 20,000 30,000 40,000 50,000 60,000
value, in dollars 18,525 17,850 16,625 15,125 13,975 13,150
(a) what was the per - mile change in the value of the car between 20,000 mi and 30,000 mi? round to the nearest cent per mile. (note: a negative average rate of change denotes a decrease.)
cents per mile
(b) write a sentence explaining the meaning of the answer to part (a).
the value of the car decreases by ____ cents for each mile driven.

Explanation:

Step1: Calculate the difference in value

The value at \(20000\) miles is \(V_1 = 17850\) dollars and the value at \(30000\) miles is \(V_2=16625\) dollars. The difference in value \(\Delta V=V_2 - V_1=16625 - 17850=- 1225\) dollars.

Step2: Calculate the difference in mileage

The difference in mileage \(\Delta M = 30000 - 20000 = 10000\) miles.

Step3: Calculate the per - mile change

The per - mile change (average rate of change) is \(\frac{\Delta V}{\Delta M}\). Since \(\Delta V=-1225\) dollars and \(\Delta M = 10000\) miles, and we want the result in cents per mile. We know that \(1\) dollar \( = 100\) cents. So \(\frac{-1225\times100}{10000}=\frac{- 122500}{10000}=-12.25\) cents per mile.

Answer:

a) \(-12.25\) cents per mile
b) The value of the car decreases by \(12.25\) cents for each mile driven.