Comparing discrete and continuous models. In a fictitious metropolitan area, residents can be divided into those who live in the city and those who live in the suburbs. Suppose C(t) gives the number of people living in the city at time t, and S(t) gives the number of people living in the suburbs, where t is measured in years. Each year, approximately 10% of the city dwellers move to the suburbs, while 20% of the suburban residents move to the city.(4) (a) Write a discrete dynamical system that models the situation. That is, find formulas for C(t 1) and S(t 1) in terms of C(t) and S(t). (Here, you should assume that exactly 10% of the city dwellers move to the suburbs each year, while exactly 20% of the suburban residents move to the city.) (b) To model this as a continuous dynamical system, we look at the rate of change in the number of people per year (after all, this is what the derivative means). For instance, the rate of change of the number of city dwellers per year is approximately 0.1C(t) 0.2S(t) because 10% of the city dwellers (0.1C(t)) move away from the city each year, while 20%