Chapter 9.1, Problem 65E

(A)

To determine

To show: The equation $N\left(t\right)=200-C{e}^{-0.5t}$ is the general solution of the differential equation $\frac{dN}{dt}=100-0.5N$ and evaluate $\overline{N}=\underset{t\to \infty }{\lim }N\left(t\right)$.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions $N\left(0\right)=50$ and $N\left(0\right)=300$.

(C)

To determine

To discuss: The long-term behavior of the population of the bacteria.