Question

Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula: a1 = 8 an = 2.9an – 1 – 0.2(an – 1)^2 Which of the following describes what is happening to the insect population for the first five years?

Answer 1

D.) The population alternates between increasing and decreasing.

Explanation:

Answer 2

The population alternates between increasing and decreasing

Explanation:

The options of the question are

A) The population density decreases each year.

B) The population density increases each year.

C) The population density remains constant.

D) The population alternates between increasing and decreasing

we have

`a_n=2.9(a_n_-_1)-0.2(a_n_-_1)^2`

`a_1=8`

Find the value of
`a_2`

For n=2

`a_2=2.9(a_1)-0.2(a_1)^2`

`a_2=2.9(8)-0.2(8)^2=10.4`

Find the value of
`a_3`

For n=3

`a_3=2.9(a_2)-0.2(a_2)^2`

`a_3=2.9(10.4)-0.2(10.4)^2=8.528`

For n=4

`a_4=2.9(a_3)-0.2(a_3)^2`

`a_4=2.9(8.528)-0.2(8.528)^2=10.1858`

For n=5

`a_5=2.9(a_4)-0.2(a_4)^2`

`a_5=2.9(10.1858)-0.2(10.1858)^2=8.7887`

therefore

The population alternates between increasing and decreasing