. Under certain circumstances a rumor spreads according to the equation 16 p(t) NOV 20 = 1 1 + ae I where p(t) is the proportion of the population that has heard the rumor at time t and a and k are positive constants. (a) Find lim, p(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. -kt A

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