Chapter 8.2, Problem 51ES

The graph of a solution to the logistic equation is known as a logistic curve, and if $y_0>0,$ it has one of four general shapes, depending on the relationship between $y_0\text{ and }L.$ In each part, assume that $k=1$ and use a graphing utility to plot a logistic curve satisfying the given condition.

$\begin{array}{l}\left(\text{a}\right)y_0>L\\ \left(\text{b}\right)y_0=L\\ \left(\text{c}\right)L/2\le y_0<L\\ \left(\text{d}\right)0<y_0<L/2\end{array}$