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 =______ hr^-1 (b) Find an expression for the number of cells after t hours. P(t) = ___________ (c) Find the number of cells after 2 hours. _______ cells

(d) Find the rate of growth after 2 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.) ________ h