Solve the Problem $\mathrm { n }$ Can Be Modeled by the Recursively Defined Sequence

question 336

Multiple Choice

Solve the problem.
-Suppose that an insect population density, in thousands, during year $\mathrm { n }$ can be modeled by the recursively defined sequence: $a _ { 1 } = 1 ; a _ { n } = 2.79 a _ { n - 1 } - 0.15 a _ { n - 1 } ^ { 2 }$ for $n > 1$ .
Use technology to graph the sequence for $n = 1,2,3 , \ldots , 20$ . Describe what happens to the population density function.

• A) The insect population stabilizes near \(8.73\) thousand.
• B) The insect population stabilizes near \(12.86\) thousand.
• C) The insect population increases every year.
• D) The insect population stabilizes near \(11.93\) thousand.

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Definitions:

Variable

1. In symbolic logic, a symbol that stands for some, but any, unnamed individual thing; 2. In statistics, a trait regarded as a generic attribute that can exist in different degrees (values).

Closed Sentence

In predicate logic, a statement in which every variable is bound by a quantifier.

Variable

An element, feature, or factor that is liable to vary or change, often used in mathematics, statistics, and scientific experiments to represent quantities or qualities that can assume different values.

Open Sentence

A mathematical or logical statement containing one or more variables that does not have a definitive truth value until the variables are specified.