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.k =(b) Find an expression for the number of cells after t hours.P(t) = (c) Find the number of cells after 8 hours.(d) Find the rate of growth after 8 hours. (Round your answer to the nearest integer.)cells/h(e) When will the population reach a million cells? (Round your answer to two decimal places.)