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 75 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k= 3 ln(2) (b) Find an expression for the number of cells after t hours. P(t) = 75e (3 ln(2)), (c) Find the number of cells after 8 hours. 125829120✓ cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) X billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr Enhanced Feedback Please try again. Remember, if the growth rate of a population, P, is proportional to the population itself, then the growth rate is given by the formula where k is the relative growth rate. Try finding k when t is measured in hours. dP dt = KP,

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