Under certain circumstances a rumor spreads according to the equation where p(t) is the proportion of the

Question:

Under certain circumstances a rumor spreads according to the equation where p(t) is the proportion of

p(1) 1 + ae-*

the population that knows the rumor at time t and a and are positive constants.
[In Section 9.5 we will see that this is a reasonable equation for p(t).]
(a) Find lim t→∞ (t).
(b) Find the rate of spread of the rumor.
(c) Graph p for the case a = 10, k = 0.5 with measured in hours. Use the graph to estimate how long it will take for 80% of the population to hear the rumor.