ANSWER
[tex]1.055 ^{20} [/tex]
times larger.
EXPLANATION
The given function is
[tex]f(x) = 1200 {(1.055)}^{x} [/tex]
The average rate of change between years 21 and 25 is
[tex] = \frac{f(25) - f(21)}{25 - 21} [/tex]
[tex] = \frac{1200 {(1.055)}^{25} - 1200 {(1.055)}^{21} }{25 - 21} [/tex]
[tex] = \frac{1200 {(1.055)}^{21} (1.055 ^{4} - 1)}{4} [/tex]
The average rate of change between years 1 and 5 is
[tex] = \frac{1200 {(1.055)}^{5} - 1200 {(1.055)}^{1} }{5 - 1} [/tex]
[tex] = \frac{1200 {(1.055)}^{1} (1.055 ^{4} - 1)}{4} [/tex]
Hence the average rate of change between years 21 and 25 is
[tex]1.055 ^{20} [/tex]
times larger than the average rate of change between years 1 and 5.
