Problem 65E

Under certain circumstances a rumor spreads according to the equation p(t)=11+aekt Where p(t) is the proportion of the population that has heard the rumor at time t and a and k are positive constants. In Section 9.4 we will see that this is a reasonable model for p(t). a Find limtp(t) b Find the rate of spread of the rumor. c Graph p for the case a=10,k=0.5 with t measured in hours. Use the graph to estimate how long it will take for 80 of the population to hear the rumor.

Step-by-Step Solution