A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 71 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = Incorrect: Your answer is incorrect. (b) Find an expression for the number of cells after t hours. P(t) = Incorrect: Your answer is incorrect. (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr