27. find the rate of change for the following. according to the graph shown, what is the rate at which a…
27. find the rate of change for the following. according to the graph shown, what is the rate at which a cars value will decrease as its mileage goes up between 20,000 miles and 40,000 miles? value of car ($) $14,000 $12,000 $10,000 $8,000 $6,000
Answer
Explanation:
Step1: Identify change in value
The car's value at 20,000 miles is $12,000 and at 40,000 miles is $6,000. The change in value $\Delta V=6000 - 12000=- 6000$.
Step2: Identify change in mileage
The change in mileage $\Delta M = 40000 - 20000 = 20000$.
Step3: Calculate rate of change
The rate of change $r=\frac{\Delta V}{\Delta M}=\frac{-6000}{20000}=-0.3$. This means the car's value decreases by $0.3$ dollars per mile. In terms of whole - dollar amounts, the car's value decreases by $300$ dollars per 1000 miles.
Answer:
The car's value decreases by $300$ dollars per 1000 miles.