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 68 cells. Find the relative growth rate. (Assume t is measured in hours.)
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Shaiju T.
A common inhabitant of the 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 53 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = 2.07944 (b) Find an expression for the number of cells after t hours. P(t) = 53e^(2.07944t) (c) Find the number of cells after 8 hours. cells = 53e^(2.07944*8) (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
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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 60 cells. (a) Find the relative growth rate. (b) Find an expression for the number of cells after $t$ hours. (c) Find the number of cells after 8 hours. (d) Find the rate of growth after 8 hours. (e) When will the population reach $20,000$ cells?
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