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Pre-Lesson: See Extra Support Materials for Algebra 1, Unit 6, Lesson 8.
In this lesson, students start to view exponential relationships as exponential functions. This means choosing an independent and dependent variable and expressing the relationships using function language and, in some cases, function notation.
For an exponential relationship, either variable can be the independent variable but one choice gives an exponential function while the other gives a logarithmic function (which is outside the scope of this course). The contexts here are chosen and presented so that it is more natural to choose an independent variable that leads to an exponential function. If students select an independent variable that would lead to a logarithmic function, recognize that their choice is valid, but that the resulting function is not the focus of this unit and that they should consider the other variable as independent here.
Students use variables to represent one real-world quantity as a function of another, which is an example of decontextualizing and reasoning abstractly (MP2).