$6$:$42$

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The following is based on a textbook problem.

Assume $9$ people originally have the virus and that in early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of $1\mathrm{.}09.$ Assume further that in the long run, they estimate approximately $6500$ people will be infected.

$($You may wish to sketch a graph of your logistic function $P=\frac{L}{1+C{e}^{-kt}}$ to help you understand this situation and answer the questions below.$)$

$($a$)$ What should we use for the parameters $k$ and $L?$

$k=$

$L=$

$($b$)$ Use the fact that when $t=0,$ we have $P=9,$ to find $C.$

$C=$

$($c$)$ What is the value of $P$ when the rate at which people are becoming infected peaks?

$P=$

When does this occur?

$t=$

Answers