The evolution of a population of bacteria (in average number per Petri dish) to which a nutrient is supplied can be described by N(t)=5,200+30,000t105+t2 where t represents the time that has elapsed in hours. In order to determine the maximum population on t0 , please answer the following questions. a) Calculate the derivative of N . Find the strictly positive critical point p of N What is the maximum population size and when will it reach this value