the following table shows the mileage on and corresponding value of a used 2004 mini cooper, 2 - door…

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. \nmileage 10,000 20,000 30,000 40,000 50,000 60,000\nvalue, in dollars 18,525 17,850 16,625 15,125 13,975 13,150\n(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.)\ncents per mile\n(b) write a sentence explaining the meaning of the answer to part (a).\nthe value of the car decreases by ____ cents for each mile driven.

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. \nmileage 10,000 20,000 30,000 40,000 50,000 60,000\nvalue, in dollars 18,525 17,850 16,625 15,125 13,975 13,150\n(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.)\ncents per mile\n(b) write a sentence explaining the meaning of the answer to part (a).\nthe value of the car decreases by ____ cents for each mile driven.

Answer

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.