A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 65 cells.

(a) Find the relative growth rate.

(b) Find an expression for the number of cells after t hours.

(c) Find the number of cells after 6 hours.

(d) Find the rate of growth after 6 hours

(e) When will the population reach 20,000 cells