A certain rumor spreads through a community at the rate of 2 (1 ) dy/dt=2y (1-y), where y is the proportion of the population that has heard the rumor at time t. a. What proportion of the community has heard the rumor when it is spreading the fastest?(a) 2y(1-y)=2y-2y^2 is largest when 2-4y=0so proportion is y= 1-2