In this lesson, students continue to examine situations characterized by exponential decay. The emphasis here is on analyzing graphs representing such situations. Students work across representations: from graphs to equations and from verbal descriptions to graphs. In addition to interpreting mathematical representations in context (MP2), students also think carefully about how the numbers used in place of \(a\) and \(b\) in an expression of the form \(a \boldcdot b^x\) influence the graph of the equation \(y = a \boldcdot b^x\) (MP7).
- Determine whether situations are characterized by exponential growth or by exponential decay given descriptions and graphs.
- Use graphs to compare and contrast situations that involve exponential decay.
- Use information from a graph to write an equation that represents exponential decay.
Let's compare situations where quantities change exponentially.
Make copies of the blackline master for the Matching Descriptions to Graphs activity, one copy for every 2 students. Cut up the slips and separate into sets ahead of time.
- I can use graphs to compare and contrast situations that involve exponential decay.
- I can use information from a graph to write an equation that represents exponential decay.
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.