Under certain circumstances a rumor spreads according to theequation: p(t) = 1/(1+ae^(-kt)) where p(t) is the proportion of thepopulation that knows the rumor at time t and a and k are positiveconstants.
a) Find limit as t approaches infinity.
b) Find the rate of spread of the rumor.
c) Graph p for the case a=10, k=0.5 with t measured inhours. Use the graph to estimate how long it will take for80% of the population to hear the rumor.
