Question

The function f(x)=1200(1.055)x models the balance of an investment x years after it is made. How does the average rate of change between years 21 and 25 compare to the average rate of change between years 1 and 5?

Answer 1

The answer is its 3 times the rate between years 1 and 5.

Answer 2

Average rate of change between years 21 and 25 is 220.547475

Average rate of change between years 1 and 5 is 75.588

Explanation:

We are given

The function models the balance of an investment x years after it is made

`f(x)=1200(1.055)^x`

Average rate of change between 21 and 25 years:

We can use formula

`A=(f(b)-f(a))/(b-a)`

now, we can plug values

`A=(f(25)-f(21))/(25-21)`

`f(25)=1200(1.055)^(25)=4576.0708`

`f(21)=1200(1.055)^(21)=3693.8809`

now, we can plug values

`A=(4576.0708-3693.8809)/(25-21)`

`A=220.547475`

Average rate of change between 1 and 5 years:

We can use formula

`A=(f(b)-f(a))/(b-a)`

now, we can plug values

`A=(f(5)-f(1))/(5-1)`

`f(5)=1200(1.055)^(5)=1568.352`

`f(1)=1200(1.055)^(1)=1266`

now, we can plug values

`A=(1568.352-1266)/(5-1)`

`A=75.588`