Barrons AP Calculus

BC  ONLY

Figure  N9–10

Figure N9–10 shows the slope field for equation (3), with k = 0.00179, which
was obtained by solving equation (5) above. Note that the slopes are the same
along any horizontal line, and that they are close to zero initially, reach a
maximum at P = 500, then diminish again as P approaches its limiting value,

1000. We have superimposed the solution curve for P(t) that we obtained in (6)
      above.

Example 21 __

Suppose a flu-like virus is spreading through a population of 50,000 at a rate
proportional both to the number of people already infected and to the number