Chapter 5.4, Problem 1CYU

A sociological study was made to examine the process by which doctors decide to adopt a new drug. The doctors were divided into two groups. The doctors in group $A$ had little interaction with other doctors and so received most of their information through mass media. The doctors in group $B$ had extensive interaction with other doctors and so received most of their information through word of mouth. For each group, let $f\left(t\right)$ be the number who have learned about the new drug after t months. Examine the appropriate differential equations to explain why the two graphs were of the types shown in Fig. 6. (Source: Sociometry.)

Figure 6 Results of a sociological study.