The growth rate of escherichia coli, a common bacterium found in the human intestine, is proportional to its size. under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 15 min. (a) if the initial population is 500, determine the function q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes).