Chapter 5.4, Problem 11E

Spread of News A news item is broadcast by mass media to a potential audience of 50,000 people. After $t$ days, $f\left(t\right)=50,000\left(1-e^{-0.3t}\right)$ people will have heard the news. The graph of this function is shown in Fig. 8.

Figure 8

a. How many people will have heard the news after $10$ days?

b. At what rate is the news spreading initially?

c. When will $22,500$ people have heard the news?

e. Approximately when will the news spread at the rate of $2500$ people per day?

e. Use equations (3) and (4) to determine the differential equation satisfied by $f\left(t\right)$.

f. At what rate will the news spread when half the potential audience has heard the news?