Lesson 5

Representing Exponential Decay

Lesson Narrative

In this lesson, students examine more situations with quantities that decrease exponentially. They work from an equation to a graph and from a graph to an equation. In both cases, they interpret the different parts of their equation in terms of the situation and use the graph to answer questions.

Like many activities in this unit, the equations and graphs represent actual quantities (the area covered by algae and the amount of insulin in a person’s body) and are to be interpreted in context (MP2). They also use a discrete graph to answer questions about quantities that vary continuously with time. In following lessons we will represent situations where the domain is all real numbers with a continuous graph.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

Learning Goals

Teacher Facing

  • Calculate growth factor using points on a graph that represents exponential decay.
  • Graph equations that represent quantities that change by a growth factor between 0 and 1.
  • Interpret equations and graphs that represent exponential decay situations.

Student Facing

Let’s think about how to show and talk about exponential decay.

Required Preparation

If possible, acquire devices that can run Desmos (recommended) or other graphing technology as an option for students to select during the lesson.

Learning Targets

Student Facing

  • I can explain the meanings of $a$ and $b$ in an equation that represents exponential decay and is written as $y=a \boldcdot b^x$.
  • I can find a growth factor from a graph and write an equation to represent exponential decay.
  • I can graph equations that represent quantities that change by a growth factor between 0 and 1.

CCSS Standards

Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In