Chapter 8.2, Problem 30ES

A cell of the bacterium E. coli divides into two cells every 20 minutes when placed in a nutrient culture. Let $y=y\left(t\right)$ be the number of cells that are present t minutes after a single cell is placed in the culture. Assume that the growth of the bacteria is approximated by an exponential growth model.

(a) Find an initial-value problem whose solution is $y(t).$

(b) Find a formula for $y\left(t\right).$

(c) How many cells are present after 2 hours?

(d) How long does it take for the number of cells to reach 1,000,000?