Unit 5: Exponential Functions and Equations

Students extend exponential functions to rational and continuous inputs, introduce logarithms as a way to solve exponential equations, study the constant e, and use exponential and logarithmic functions and their graphs to model and solve problems.

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Unit

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Concept

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Practice

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Set 1

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Advanced

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What this unit covers

A Growing and Shrinking · 7 lessons

Goals

• Interpret the meaning of a rational input to an exponential function in context.
• Understand that an exponential function changes by a constant factor over equal intervals.

Lessons

1. Growing and Shrinking
2. Representations of Growth and Decay (Optional)
3. Understanding Rational Inputs
4. Representing Functions at Rational Inputs
5. Changes Over Rational Intervals
6. Writing Equations for Exponential Functions
7. Interpreting and Using Exponential Functions (Optional)

B Missing Exponents · 4 lessons

Goals

• Create equivalent equations in exponential and logarithmic forms.
• Estimate the value of a logarithmic expression.

Lessons

1. Unknown Exponents
2. What Is a Logarithm?
3. Interpreting and Writing Logarithmic Equations
4. Evaluating Logarithmic Expressions

C The Constant e · 3 lessons

Goals

• Interpret the parameters in the equations of exponential functions with the form a · e^(kt).

Lessons

1. The Number e
2. Exponential Functions with Base e
3. Solving Exponential Equations

D Logarithmic Functions and Graphs · 3 lessons

Goals

• Use graphs and logarithms to calculate or estimate solutions to exponential equations.

Lessons

1. Using Graphs and Logarithms to Solve Problems (Part 1)
2. Using Graphs and Logarithms to Solve Problems (Part 2)
3. Logarithmic Functions

E Let's Put It to Work · 1 lesson

Lessons

1. Applications of Logarithmic Functions (Optional)