Some epidemiologists are trying to model and predict the spread of Yersinia pestis infections in a population in sub-Saharan Africa. Current measurements estimate the the number of cases increase continuously at a rate of 5% per day. At time of first reporting, there was 50 cases found. a) Write an equation to model the number of cases N(t) where t is the number of days after first reporting. b) How many total cases are predicted to occur after 20 days c) How long would it take for instantaneous rate of increase in the number of cases to exceed 10 new cases a day.