In a sufficiently large population, the number of people x who have a certain (a) x = piece of information can be treated as a differentiable function of time t, and the rate at which the information spreads, dx (b) Half the population will have heard the information when t= days. dt is assumed to be proportional to the (Type an integer or decimal rounded to two decimal places as needed.) number of people who have the information times the number of people who do not. This leads to the equation following equation dx - = kx(N - x), where N is the number of people in the population. Suppose t is in days, k = and two people 100 share the information at time t = 0 in a population of N = 400 people. (a) Find x as a function of t. (b) When will half the population have heard the information? (This is when the rumor will be spreading the fastest.)