Assume a community haves 20,000 people susceptible to the certain contagious disease. Assume that N(0), the number of people who have the disease at time t = 0, is 1,000, and is raising at the rate of 190 per day. Suppose that the rate of change of the number of people who have disease is proportional to the product of number of people who have it and to the number of people that don't. How long will it be till half of the susceptible population is infected? If, on the other hand, we supposed that the rate of change of the disease was a constant 190 people per day, how long would it take to infect half of the population?