Question

The function f(x)=15000(0.96)^x represents the value in dollars of a vehicle x years after it has been purchased new. What is the average decrease in value per year between years 5 and 10? Please show all work!

Answer 1

To find the average decrease in value per year between years 5 and 10 of a vehicle, we plug in x=5 and x=10 into the given function, subtract the values, and divide by 5.

Step-by-step explanation:

To find the average decrease in value per year between years 5 and 10, we need to calculate the difference in value between those two years and then divide it by the number of years.

First, we find the value of the vehicle in year 5 by plugging in x = 5 into the function:

f(5) = 15000(0.96)^5

solving this equation gives us the value of the vehicle in year 5.

Next, we find the value of the vehicle in year 10 by plugging in x = 10 into the function:

f(10) = 15000(0.96)^10

solving this equation gives us the value of the vehicle in year 10.

Finally, we subtract the value in year 10 from the value in year 5 and divide by 5 (the number of years) to get the average decrease in value per year.

Answer 2

First we need to find the value of car after 5 years and after 10 years.

Value of the car after 5 years will be:

`f(5)=15000 (0.96)^(5)=12230.59`

Value of the car after 10 years will be:

`f(10)=15000 (0.96)^(10)=9972.49`

The decrease in the value of car will be:

`f(5)-f(10)=2258.10`

Average decrease in the value of car will be:

`(2258.10)/(10-5)=451.62`

Thus, on average the value of car decreases by $451.62 between year 5 and 10.