007A Sample Midterm 2, Problem 4

Assume  $N(t)$  denotes the size of a population at time  $t$  and that  $N(t)$  satisfies the equation:

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

Let  $f(N)=3N{\bigg (}1-{\frac {N}{20}}{\bigg )},~N\geq 0.$  Graph  $f(N)$  as a function of  $N$  and identify all equilibria. That is, all points where  ${\frac {dN}{dt}}=0.$

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