Unit 6: Introduction to Exponential Functions

Students build on their understanding of linear functions, properties of exponents, and percent change to explore exponential relationships, write and graph exponential functions, and compare them with linear functions.

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Concept

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What this unit covers

A Looking at Growth · 2 lessons

Goals

• Compare linear and exponential relationships by performing calculations.
• Describe patterns in tables that represent linear and exponential relationships.

Lessons

1. Growing and Growing
2. Patterns of Growth

B A New Kind of Relationship · 5 lessons

Goals

• Interpret a negative exponent in equations that represent exponential growth or decay.
• Write an equation to represent a quantity that changes by a growth factor.
• Write and graph an equation that represents exponential decay to solve problems.

Lessons

1. Representing Exponential Growth
2. Representing Exponential Decay
3. Understanding Decay
4. Analyzing Graphs
5. Using Negative Exponents

C Exponential Functions · 6 lessons

Goals

• Describe the effect of changing parameters on a graph that represents an exponential function.
• Use function notation to write equations that represent exponential relationships.

Lessons

1. Exponential Situations as Functions
2. Interpreting Exponential Functions
3. Looking at Rates of Change
4. Modeling Exponential Behavior
5. Reasoning about Exponential Graphs (Part 1)
6. Reasoning about Exponential Graphs (Part 2) (Optional)

D Percent Growth and Decay · 5 lessons

Goals

• Calculate the result of repeated percent increase for the same initial balance and interest rate, but compounded at different intervals.
• Justify why applying a percent increase n times is not equivalent to applying the percent n times.

Lessons

1. Recalling Percent Change (Optional)
2. Functions Involving Percent Change
3. Compounding Interest
4. Different Compounding Intervals
5. Expressed in Different Ways

E Comparing Linear and Exponential Functions · 2 lessons

Goals

• Use rates of change, and show that, for any equal intervals of the independent variable, an exponential function always increases or decreases by an equal factor.
• Use tables, calculations, and graphs to compare growth rates of linear and exponential functions.

Lessons

1. Which One Changes Faster?
2. Changes over Equal Intervals

F Let's Put It to Work · 1 lesson

Lessons

1. Predicting Populations