3.1. Exponential growth. For an epidemic, the basic reproduction number, denoted Ro, is the average number of people that each person with the disease infects, assuming only a small fraction of the population has been previously infected and no measures are taken to limit the disease's spread (e.g., social distancing, mask wearing, vaccination) are taken. If the typical time from when a person contracts the disease to when s/ he stops being infectious is T (days) then for each infected person now, there will be roughly Ro infected people after time T, R infected people after time 27, and so on. (Actually, the situation is a little more complicated, but this is a reasonable approximation.) This exponential growth stops when either a large fraction of the population (as compared to 1-1/Ro) has been infected or steps are taken to prevent disease transmission. Let's approximate the average time from when a person is exposed to coronavirus to when they're no longer infectious as 7 days. (This is substantially shorter than the CDC guidelines, but probably a person spreads the disease most before they're very sick. Once you're fairly sick, you stay home, and even if you're contagious you spread it to fewer people.) So, we'll assume T = 7 days. (Q3.1) If N people are infected with coronavirus at time 0 and no measures are taken to prevent transmission (as in the model just discussed), how many people will be infected t days in the future? Your answer should be in terms of N, Ro, and t. (Hint: if N are infected at time 0 then NRo are infected after 2 weeks. How many are infected after t weeks? Your answer should be an exponential function of the form abct where a, b, and c are constants, written in terms of N and Ro.) (Q3.2) Rewrite your answer to the previous part in the form melt where m and k are constants, written in terms of N and Ro. (Q3.3) Find the instantaneous rate of change in coronavirus infections at time t. Include your units