vehicles lose value over time. A car is purchased for $23 500, but it is worth only $8750 after eight years. What is the average annual rate of change in the value of the car, as a percent?
To find the average annual rate of change in the value of the car, you need to calculate the difference in value over the given time period and then express it as a percentage.
First, calculate the change in value by subtracting the final value from the initial value:
Change in value = Final value - Initial value
Change in value = $8,750 - $23,500
Change in value = -$14,750
The negative sign indicates that the value has decreased over time.
Next, calculate the average annual rate of change by dividing the change in value by the number of years:
Average annual rate of change = Change in value / Number of years
Average annual rate of change = -$14,750 / 8
Average annual rate of change = -$1,843.75
Now, express this value as a percentage:
Percentage change = (Average annual rate of change / Initial value) * 100
Percentage change = (-$1,843.75 / $23,500) * 100
Percentage change ≈ -7.85%
Therefore, the average annual rate of change in the value of the car is approximately -7.85%. This indicates a decrease in value over time.
avg rate of change = (23500 - 8750)/(8
= ...