Question

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?

Answer 1

The answer is 3.375

Step-by-step explanation:

Answer 2

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

Step-by-step 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.