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

ANSWER


`1.055 ^(20)`

times larger.


Step-by-step explanation


The given function is



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


The average rate of change between years 21 and 25 is


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





`= \frac{1200 {(1.055)}^(25) - 1200 {(1.055)}^(21) }{25 - 21}`



`= \frac{1200 {(1.055)}^(21) (1.055 ^(4) - 1)}{4}`



The average rate of change between years 1 and 5 is


`= \frac{1200 {(1.055)}^(5) - 1200 {(1.055)}^(1) }{5 - 1}`



`= \frac{1200 {(1.055)}^(1) (1.055 ^(4) - 1)}{4}`



Hence the average rate of change between years 21 and 25 is

`1.055 ^(20)`

times larger than the average rate of change between years 1 and 5.