Under certain circumstances, a rumor spreads according to the equation [math] where [math] is the proportion of the population that knows the rumor at time [math], and [math] and [math] are positive constants.
(a) Find [math].
(b) Find the rate of speed of the rumor.
(c) How long will it take for 80% of the population to hear the rumor? Here, take [math] with [math] measured in hours.

(a) limit [math]
(b) [math]
(c) hours