Question

The growth rate of the bacterium Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every $20 \mathrm{~min}$. a. If the initial cell population is 100 , determine the function $Q(t)$ that expresses the exponential growth of the number of cells of this bacterium as a function of time $t$ (in minutes). b. How long will it take for a colony of 100 cells to increase to a population of 1 million? c. If the initial cell population were 1000 , how would this alter our model?

          The growth rate of the bacterium Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every $20 \mathrm{~min}$.
a. If the initial cell population is 100 , determine the function $Q(t)$ that expresses the exponential growth of the number of cells of this bacterium as a function of time $t$ (in minutes).
b. How long will it take for a colony of 100 cells to increase to a population of 1 million?
c. If the initial cell population were 1000 , how would this alter our model?

Added by Jennifer P.

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