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Algebra 1

5.12.0 Lesson Overview

Algebra 15.12.0 Lesson Overview

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In this lesson, you will analyze the graph of an exponential function ff given by f(x)=a·bxf(x)=a·bx. In particular, you study the effect of bb on the shape of the graph. To observe how bb impacts the shape of the graph when b>1b>1 and when 0<b<10<b<1, you simultaneously examine several functions of this form, all of which have the same value of aa.

These lessons encourage greater attention to the growth factors of the different functions, rather than on interpreting the quantities in context. Since you are focusing mainly on understanding how varying bb impacts the graph, you are looking at the structure of an exponential function and its graph.

When you finish this lesson, you will be able to:

  • Describe the effect of changing aa and bb on a graph that represents f(x)=a·bxf(x)=a·bx.
  • Use equations and graphs to compare exponential functions.

Here are the activities that will help you reach those goals:

  • 5.12.1: Modeling Exponential Decay
  • 5.12.2: Equations and Their Graphs
    • 5.12.2: Self Check
    • 5.12.2: Additional Resources
  • 5.12.3: Graphs Representing Exponential Decay
    • 5.12.3: Self Check
    • 5.12.2: Additional Resources
  • 5.12.4: Possible Equation for a Function on a Graph
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