Graph the Function Corresponding to the Sequence Defined $n$ Can Be Modeled by the Recursively Defined Sequence

question 317

Multiple Choice

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-Suppose that an insect population density, in thousands, during year $n$ can be modeled by the recursively defined sequence: $a _ { 1 } = 1 ; a _ { n } = 2.67 a _ { n - 1 } - 0.17 a \underset { n - 1 } { 2 } \quad$ 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 \(6.62\) thousand.
• B) The insect population stabilizes near \(9.82\) thousand.
• C) The insect population increases every year.
• D) The insect population stabilizes near \(10.75\) thousand.

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