2 years ago

Need help with the problem.

Mathematics

1 answer:

pshichka [43]2 years ago

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Answer 40% passed

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Step-by-step explanation:

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Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula: a1 =

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The population alternates between increasing and decreasing

Step-by-step 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

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