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Sergio [31]
3 years ago
9

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?
Mathematics
2 answers:
vlabodo [156]3 years ago
7 0

Answer:

The population alternates between increasing and decreasing

Step-by-step explanation:

<u><em>The options of the question are</em></u>

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

lys-0071 [83]3 years ago
6 0

Answer:

D.) The population alternates between increasing and decreasing.

Step-by-step explanation:

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