Question

The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.

How does the average rate of change between Years 1 and 5 compare to the average rate of change between Years 11 and 15?

The average rate of change is about 13
as fast in Years 1 to 5.

The average rate of change is about 3 times as fast in Years 1 to 5.

The average rate of change is about 12
as fast in Years 1 to 5.

The average rate of change is 2 times as fast in Years 1 to 5.

Answer 1

Answer: (B) 3 times as fast

Explanation:

rate of change is the "slope" between the given interval.

f(x) = 125(.9)ˣ

f(1) = 125(.9)¹

= 112.5

f(5) = 125(.9)⁵

= 73.8

`(f(5) - f(1))/(5 - 1) = (73.8-112.5)/(5-1) = -(38.7)/(4) = -9.675`

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f(11) = 125(.9)¹¹

= 39.2

f(15) = 125(.9)¹⁵

= 25.7

`(f(15) - f(11))/(15 - 11) = (39.2-25.7)/(15-11) = -(13.5)/(4) = -3.375`

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The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.