Question

The function

f(x)=18000(0.52)x
 represents the value in dollars of a vehicle x years after it has been purchased new.
What is the average rate of change in value per year between years 4 and 8?
 


​​
−$18000/year

​​
−$1219.87/year


−$304.97/year

−$0.52/year

Answer 1

304.97/year

Step-by-step explanation

We know that the rate of change of function=

Thus, for the required situation the rate of change of function per year between years 4 and 8=

Hence the average rate of change in value per year between years 4 and 8= -$304.97 per year.

Answer 2

Answer: −$304.97/year

Explanation:

We know that the rate of change of function=
`(f(x_2)-f(x_1))/(x_2-x_1)`

Thus, for the required situation the rate of change of function per year between years 4 and 8=

`(f(8)-f(4))/(8-4)\\\\=(18000(0.52)^8-18000(0.52)^4)/(4)\\\\=(18000[(0.52)^8-(0.52)^4])/(4)\\\\=(18000[0.00534-0.07311])/(4)\\\\=(18000*-0.06777)/(4)\\\\=(-1219.86)/(4)=-304.97`

Hence the average rate of change in value per year between years 4 and 8= -$304.97 per year.