A rumor is spread in a school. For 0 < a < 1 and b > 0, the time t at which a fraction p of the school population has heard the rumor is given by t(p) = [ " b dx. x(1 - x) dz (a) Evaluate the integral to find an explicit formula for t(p). Write your answer so it has only one In term. b Sa z(1-2) dx = (b) At time t = 0, one percent of the school population (p = 0.01) has heard the rumor. What is a? a (c) At time t = 1, fifty-one percent of the school population (p = 0.51) has heard the rumor. What is b? b = (d) At what time has ninety-five percent of the population (p = 0.95) heard the rumor? t =