Chapter 4.1, Problem 14E

Reminder Round all answers to two decimal places unless otherwise indicated.

Growth of Bacteria The organism E. coli is a common bacterium. Under certain conditions, it undergoes cell division approximately each $20\text{minutes}$. During cell division, each cell divides into two cells.

a. Explain why the number of E. coli cells present is an exponential function of time.

b. What is the hourly growth factor for E. coli?

c. Express the population $N$ of E. coli as an exponential function of time $t$ measured in hours. (Use $N_0$ to denote the initial population.)

d. How long will it take a population of E. coli to triple in size?