Exercise 1.4.30

Question

A gray squirrel population was introduced in a certain region 18 years ago. Biologists observe that the population doubles every six years, and now the population is 600 .

\begin{enumerate}[label=(\alph*)]
\item What was the initial squirrel population?

\item  What is the expected squirrel population $t$ years after introduction?

\item  Estimate the expected squirrel population 10 years from now.
\end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item Since the grey squirrel population doubles every six years, the population has increased by $2^{18 / 6}=2^{3}=8$ times for 18 years. Therefore, the initial squirrel population was $600: 8=75$.

\item  We define the population function $p$ of time t as follows:

$$
\forall t \in[0,+\infty): \quad p(t)  = 75 \cdot 2^{t / 6} 	ext {. }
$$

\item  For $t=10+18=28$, we have:

$$
p(28)=75 \cdot 2^{28 / 6} \approx 1904 	ext {. }
$$
\end{enumerate}

Exercise 1.4.30

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Exercise 1.4.30

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