Chapter 10.6, Problem 3E

In Exercises 1- 4, you are given a logistic equation with one more initial conditions.

(a) Determine the carrying capacity and intrinsic rate.

(b) Sketch the graph of $\frac{dN}{dt}$ versus $N$ in an $Nz$-plane.

(c) In the $tN$-plane, plot the constant solutions and place a dashed line where the concavity of certain solution may change.

(d) Sketch the solution curve corresponding to each given initial condition.

$\frac{dN}{dt}=-.01N^2+N,N(0)=5$