A Rumor Tends to Spread According to the Logistic Differential $\frac { d y } { d t } = 0.3 y - 0.0001 y ^ { 2 }$

Essay

A rumor tends to spread according to the logistic differential equation $\frac { d y } { d t } = 0.3 y - 0.0001 y ^ { 2 }$ , where y is the number of people in the community who have heard the rumor and t is the time in days.(a) Describe the population for this sociological study.(b) Assume that there were 10 people who knew the rumor at initial time t = 0. Find the solution for the differential equation.(c) How many days will it take for half of the population to hear the rumor?