Growth of Bacteria 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 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)= 500e 0.0347t X (b) How long would it take for a colony of 500 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.) 219.04 ✔min (c) If the initial cell population were 5000, what is our model? Q(t) = 50000.0347t X