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.
- 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.
Let’s think about how to show and talk about exponential decay.
If possible, acquire devices that can run Desmos (recommended) or other graphing technology as an option for students to select during the lesson.
- 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.
In an exponential function, the output is multiplied by the same factor every time the input increases by one. The multiplier is called the growth factor.