A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich,who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells. (a) Find the relative growth rate. (b) Find an expression for the number of cells after t hours. (c) Find the number of cells after 2 hours. (d) Find the rate of growth after 2 hours. (e)When will the population reach a million cells?