under certain circumstances a rumor spread according to the equation: p(t) = 1/(1+ae^(-kt)) where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants.
(a) find limit as t approaches infinity of 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.

Question

under certain circumstances a rumor spread according to the equation: p(t) = 1/(1+ae^(-kt)) where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants.
(a) find limit as t approaches infinity of 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.