Chapter 9.3, Problem 46E

(a)

To determine

To solve: The given initial value problem in terms of $k\text{ and }{y}_0$.

(b)

To determine

To sketch: The given function $y=\frac{y_0}{\left(1-y_0\right)e^{-kt}+y_0}$ for $k=0.3,y_0=0.1\text{ and }{y}_0=0.7$.

(c)

To determine

To describe: The long term behavior of the rumor function $y^{\prime }\left(t\right)=ky\left(1-y\right)$.