# 007A Sample Midterm 2, Problem 4

Assume  ${\displaystyle N(t)}$  denotes the size of a population at time  ${\displaystyle t}$  and that  ${\displaystyle N(t)}$  satisfies the equation:
${\displaystyle {\frac {dN}{dt}}=3N{\bigg (}1-{\frac {N}{20}}{\bigg )}.}$
Let  ${\displaystyle f(N)=3N{\bigg (}1-{\frac {N}{20}}{\bigg )},~N\geq 0.}$  Graph  ${\displaystyle f(N)}$  as a function of  ${\displaystyle N}$  and identify all equilibria. That is, all points where  ${\displaystyle {\frac {dN}{dt}}=0.}$