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Question

Apply the logistic growth model with the following sets of values to find the population in the next four generations. Be sure to round the population each year to the nearest integer.\

$N=4000, k=2.5, a_1=1800$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 4$\textbf{Given.}$ The logistic growth equation is the recursion defined by:

$a_{n+1} = f(a_n) = k\left( 1 - \dfrac{a_n}{N}\right)a_n$

where $k$ is the growth rate constant and $N$ is the maximum size of the population. We are tasked to find the size of the next four generations which are $a_2$, $a_3$, $a_4$, and $a_5$ through four iterations of the given value for $a_1$. We are given:

$N = 4000,\;k=2.5,\;a_1=1800$

A calculator or spreadsheet may help in the calculations.

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