007A Sample Midterm 2, Problem 4

Assume  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle N(t)}   denotes the size of a population at time  $t$  and that  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle N(t)}   satisfies the equation:

${\frac {dN}{dt}}=3N{\bigg (}1-{\frac {N}{20}}{\bigg )}.$

Let  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f(N)=3N{\bigg (}1-{\frac {N}{20}}{\bigg )},~N\geq 0.}   Graph  $f(N)$  as a function of  $N$  and identify all equilibria. That is, all points where  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {dN}{dt}}=0.}

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