Chapter 4.4, Problem 194E

The following questions consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells.

194. The Gompertz equation is given by $P(t)\text{'}=\alpha \text{In}\left(\frac{K}{P(t)}\right)P(t)$. Draw the directional fields for this equation assuming all parameters are positive, and given that K=1.