Alg1.5 Introduction to Exponential Functions
In this unit, students are introduced to exponential relationships. Students learn that exponential relationships are characterized by a constant quotient over equal intervals, and compare them to linear relationships which are characterized by a constant difference over equal intervals. They encounter contexts with quantities that change exponentially. These contexts are presented verbally and with tables and graphs. They construct equations and use them to model situations and solve problems. They learn that the output of an increasing exponential function is eventually greater than the output of an increasing linear function for the same input.
Students view these new types of relationships as functions and employ the notation and terminology of functions (for example, dependent and independent variables). They study graphs of exponential functions both in terms of contexts they represent and abstract functions that don’t represent a particular context, observing the effect of different values of \(a\) and \(b\) on the graph of the function \(f\) represented by \(f(x)=ab^x\). The context of credit (both in terms of loans and savings) is used through several lessons.