1. Re-work Problem #4 in the First Midterm Exam assuming that no more than two hundred thousand people can be infected with the virus. Determine also how long it will take for the number of infected people to reach 190,000. 4. A new virus strain starts out with one infected individual and passes on to others in such a way that the rate of infection is proportional to the number of infected individuals. If the number of infected individuals triples every four days, set up and solve an initial value problem to determine to how long it will take for the number of infected individuals to reach 100,000. Assume that there is no deterrent for the spread of the virus. 1. Re-work Problem #4 in the First Midterm Exam assuming that no more than two hundred thousand people can be infected with the virus. Determine also how long it will take for the number of infected people to reach 190,000. 4. A new virus strain starts out with one infected individual and passes on to others in such a way that the rate of infection is proportional to the number of infected individuals. If the number of infected individuals triples every four days, set up and solve an initial value problem to determine to how long it will take for the number of infected individuals to reach 100,000. Assume that there is no deterrent for the spread of the virus