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 40 cells. (a) Find the relative growth rate. k= 3 ln (2) hr-1 (b) Find an expression for the number of cells after t hours. 40(231) P(t) = (c) Find the number of cells after 3 hours. 20480 cells (d) Find the rate of growth after 3 hours. (Round your answer to the nearest integer.) 42587 cells/h (e) When will the population reach a million cells? (Round your answer to two decimal places.) 5.98 h

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