The growth rate of 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 min.

Question

The growth rate of 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 min.
(a) If the initial population is 1000, 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 1000 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.)
min

(c) If the initial cell population were 10000, what is our model?
Q(t) =