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 b t(p) = ₁² z(1²-2) x x) a dx. (a) Evaluate the integral to find an explicit formula for t(p). Write your answer so it has only one In term. Sa x(1-x) 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 percent of the school population (p = 0.5) has heard the rumor. What is b? b = (d) At what time has ninety-four percent of the population (p = 0.94) heard the rumor? t

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