The function

f (x) = 60

(1.5)

x

models an animal population after x years.

How does the average rate of change between Year 3 and Year 6 compare to the average rate of change between Year 0 and Year 3?

The rate of change in the 2nd 3-year interval is 3.375 times that in the 1st 3-year interval.

Explanation:

The exponential function tells you that each year values get multiplied by 1.5. Then after thee years, values are multiplied by 1.5³ = 3.375. This is true for all function values, including average rate of change. Whatever the rate of change is in years 0-3, it will be 3.375 times that in years 3-6.

The calculation performed by the graphing calculator confirms this:

... the average rate of change in years 3-6 is 160.3125; in years 0-3, it is 47.5.

The ratio of these average rate of cange values is 3.375.