Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation $\frac{dN}{dt}=-N^2+N$ with the initial condition $N\left(0\right)=0.5$.

(b)

To determine

To graph: The function $\frac{dN}{dt}=-N^2+N$ versus $N$ in an $Nz$-plane.

(c)

To determine

To graph: The constant solution of $\frac{dN}{dt}=-N^2+N$ in $tN$-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation $\frac{dN}{dt}=-N^2+N$ corresponding to the initial condition $N\left(0\right)=0.5$.