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.
Lesson overview
 5.1 Warmup: Two Other Tables (5 minutes)

5.2 Activity: The Algae Bloom (15 minutes)
 Includes "Are you Ready for More?" extension problem
 5.3 Activity: Insulin in the Body (15 minutes)
 Lesson Synthesis
 5.4 Cooldown: Acetaminophen (5 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s think about how to show and talk about exponential decay.
Learning targets (student facing):
 I can explain the meanings \(a\) of \(b\) and in an equation that represents exponential decay and is written as \(y=a \cdot b^x\).
 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.
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.
Standards:
 This lesson builds towards the standards: CCSS.HSFBF.ACCSS.HSFIF.B.4MS.FIF.4CCSS.HSFIF.C.7.eMS.FIF.7eCCSS.HSFLE.A.2MS.FLE.2MO.A1.BF.AMO.A1.IF.B.3MO.A1.IF.C.7MO.A1.LQE.A.3
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.