In a sufficiently large population, the number of people x who have a certain piece of information can be treated as a differentiable function of time t, and the rate (a) x =] dx at which the information spreads, , is assumed to be proportional to the number of people who have the information times the number of people who do not. (b) Half the population will have heard the information when t= days. 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 (Type an integer or decimal rounded to two decimal places as needed.) dt 200 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.)