Growth of BacteriaThe 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 50, 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 50 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 500, what is our model?Q(t) =