A new virus is out of control. By the time anyone realizes the situation, there are already 1000 new cases per day. A week later there are 2000 new cases per day. A week after that there are 4000 new cases per day. l l 1 1. Take f to be time measured in weeks, with t = 0 at the point in time when the new case rate was 10001day. i Assuming no public health measures are taken and the above pattern of increase in the rate of new cases I continues, provide a formula for the rate function r(t) for new cases, in cases per day. \\ 2. Researchers looking through health records determine that by the point in time that we have designated as 1 I = 0, the number of people who had already experienced an infection was 12,500. Provide a forrnula for the- L total number of people that had experienced an infection one year later, at t = 52. (You do not need to l evaluate your formula.)