7. (7 pts) Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. It is assumed that the rate at which the virus spreads is proportional not only to the number a of infected students but also to the number of students not infected. It is observed that after 4 days, 30 students are infected. (a) Write the initial value problem that is associated with this scenario. (b) Solve the IVP and determine the number of infected students after 9 days. (c) At what time is the rate of infection the greatest