Graphs of Exponential Functions

Examples, videos, and solutions to help Algebra I students represent exponential functions on graphs.

New York State Common Core Math Algebra I, Module 1, Lesson 3

Worksheets for Algebra I, Module 1, Lesson 3 (pdf)

Student Outcomes

• Students choose and interpret the scale on a graph to appropriately represent an exponential function.
• Students plot points representing number of bacteria over time, given that bacteria grow by a constant factor over evenly spaced time intervals.

Problem Set Sample Solutions

1. Below are three stories about the population of a city over a period of time and four population-versus-time graphs. Two of the stories each correspond to a graph. Match the two graphs and the two stories. Write stories for the other two graphs, and draw a graph that matches the third story.
   Story 1: The population size grows at a constant rate for some time, then doesn’t change for a while, and then grows at a constant rate once again.
   Story 2: The population size grows somewhat fast at first, and then the rate of growth slows.
   Story 3: The population size declines to zero.
2. In the video, the narrator says:
   “Just one bacterium, dividing every minutes, could produce nearly billion billion bacteria in one day. That is bacteria.”
   This seems WAY too big. Could this be correct, or did she make a mistake? (Feel free to experiment with numbers using a calculator.)
3. Bacillus cereus is a soil-dwelling bacterium that sometimes causes food poisoning. Each cell divides to form two new cells every 30 minutes. If a culture starts out with exactly 100 bacterial cells, how many bacteria will be present after 3 hours?
4. Create a story to match each graph below:

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Exit Ticket
Assume that a bacteria population doubles every hour. Which of the following three tables of data, with representing time in hours and the count of bacteria, could represent the bacteria population with respect to time? For the chosen table of data, plot the graph of that data. Label the axes appropriately with units.

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