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The growth rate of the bacterium Escherichia Coli, a common bacterium found in the human intestine, is proportional to its size. Under idea laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. (a) If the initial population is 500 , determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes). Q(t) = (b) How long would it take for a colony min 500 cells to increase to a population of 1 million? (c) If the initial cell population were 5000, what is our model?

The growth rate of the bacterium Escherichia Coli, a common bacterium found in the human intestine, is proportional to its size. Under idea laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. (a) If the initial population is 500 , determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes). Q(t) = (b) How long would it take for a colony min 500 cells to increase to a population of 1 million? (c) If the initial cell population were 5000, what is our model?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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The growth rate of the bacterium Escherichia Coli, a common bacterium found in the human intestine, is proportional to its size. Under idea laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. (a) If the initial population is 500 , determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes). Q(t) = (b) How long would it take for a colony of 500 cells to increase to a population of 1 million? min (c) If the initial cell population were 5000, what is our model? Q(t) =
Transcribed Image Text:The growth rate of the bacterium Escherichia Coli, a common bacterium found in the human intestine, is proportional to its size. Under idea laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. (a) If the initial population is 500 , determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes). Q(t) = (b) How long would it take for a colony of 500 cells to increase to a population of 1 million? min (c) If the initial cell population were 5000, what is our model? Q(t) =
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