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 11 and 15 compare to the average rate of change between years 1 and 5?

The average rate of change between years 11 and 15 is about 13 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 3 times the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 12 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5.

Question

Mathematics

Abigail Henson

29 December, 23:36

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 11 and 15 compare to the average rate of change between years 1 and 5?

The average rate of change between years 11 and 15 is about 13 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 3 times the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 12 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5.

+4

Answers (1)

Know the Answer?

Maritza Koch · Answer 1

Given that the population is modeled by:

f (x) = 125 (0.9) ^x

the average rate of change will be as follows:

Year 11 and 15:

f (11) = 125 (0.9) ^11

=39.226

f (15) = 125 (0.9) ^15

=25.736

rate of change = (25.736-39.226) / (15-11)

=-3.37

year 1 and 5

f (1) = 125 (0.9) ^1

=112.5

f (5) = 125 (0.9) ^5

=73.811

rate of change:

(73.811-112.5) / 4

=-9.67

dividing the two results of rate of change we get:

-9.67/-3.37

=2.97-=3

From the above we conclude that the average rate of change between year 1 to 5 is above 3 times that of year 11 to year 15