106k views
5 votes
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.

1 Answer

3 votes

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

********************

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

********************

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

User Daniel Eberl
by
7.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories