The total number of people infected with a virus can often be modelled using the logistic growth model: The rate of change of the number of people who are infected is proportional to the product of the number of people who have been infected, y, and the number of people who have not been infected, (M 3;), dz: 7:]'3 M where k is a. constant. Suppose that time, t, is in weeks and that 10 people originally have the virus in an isolated town whose total population is 5000. In the early stages, the number of people infected is increasing exponentially with rate k = 1.78. 1. Find a. function y(t) to model the number of people infected. 2. Sketch a graph of the function y(t) that you found in part (a). Then, use your graph to estimate when the rate at which people are becoming infected starts to decrease