Answer:
Average rate of change between years 21 and 25 is 220.547475
Average rate of change between years 1 and 5 is 75.588
Step-by-step explanation:
We are given
The function models the balance of an investment x years after it is made
[tex]f(x)=1200(1.055)^x[/tex]
Average rate of change between 21 and 25 years:
We can use formula
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]
now, we can plug values
[tex]A=\frac{f(25)-f(21)}{25-21}[/tex]
[tex]f(25)=1200(1.055)^{25}=4576.0708[/tex]
[tex]f(21)=1200(1.055)^{21}=3693.8809[/tex]
now, we can plug values
[tex]A=\frac{4576.0708-3693.8809}{25-21}[/tex]
[tex]A=220.547475[/tex]
Average rate of change between 1 and 5 years:
We can use formula
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]
now, we can plug values
[tex]A=\frac{f(5)-f(1)}{5-1}[/tex]
[tex]f(5)=1200(1.055)^{5}=1568.352[/tex]
[tex]f(1)=1200(1.055)^{1}=1266[/tex]
now, we can plug values
[tex]A=\frac{1568.352-1266}{5-1}[/tex]
[tex]A=75.588[/tex]
