Lesson 6A: Exploring Exponential Functions

French biologist Jacques Monod (1910–1976) was fascinated by explaining how life works.

With colleague Francois Jacob, Monod did much to reveal the way in which genes regulate cell metabolism. For this work, the two men were awarded a Nobel Prize in 1965.

Much of Monod's exploration involved bacteria, specifically Escherichia coli (E. coli). E. coli are a large and diverse group of rod-shaped bacteria in the digestive tract of warm-blooded animals, including humans.

Many are completely harmless, but others can cause illnesses such as diarrhea, pneumonia, and urinary tract infections. Transmission of illness-causing E. coli is caused typically by improper hygiene such as not washing one's hands after using the washroom. This was the likely cause of food contamination that resulted in a major E. coli outbreak in Germany in 2011.

According to the national E. coli lab at the German Federal Instititute for Risk Assessment, the strain of bacteria responsible for the outbreak had been circulating in Germany for ten years. This outbreak caused illness to thousands and was linked to more than forty-five deaths.

In his study of E. coli, Monod wanted to know how much time would be required to fill a room with E. coli. Bacteria such as E. coli reproduce by fission. The organism divides into roughly equal halves, and in ideal conditions, it can double every twenty to thirty minutes. The number of bacteria grows exponentially, so its growth can be represented by an exponential function.

In this Training Camp, you will investigate the characteristics of exponential functions. This will prepare you for Lesson 6C in which you use exponential functions to model and solve real world problems.

By the end of this lesson, you should be able to

describe the characteristics of an exponential function by analyzing its graph
describe the characteristics of an exponential function by analyzing its equation
match the equation of an exponential function to its corresponding graph