# Chapter 3: Analyzing Exponential and Logarithmic Functions

**At Grade**Created by: CK-12

## Introduction

This chapter focuses on exploring functions where the variable is an exponent. These types of functions are commonly used to model population growth and decline, temperature change, earthquake and sound magnitude, distances between stars and sizes of microscopic particles.

Commonly, exponential and logarithmic functions are the "right tools for the job" when dealing with extremely large and extremely small things or differences between things. Bankers and investors, astronomers, biologists, all use exponential and logarithmic functions regularly in the workplace.

## Chapter Outline

- 3.1. Functions and Inverses
- 3.2. One-to-One Functions and Their Inverses
- 3.3. Basic Exponential Functions
- 3.4. Graphs of Exponential Functions
- 3.5. Logarithmic Functions
- 3.6. Graphs of Logarithmic Functions
- 3.7. Properties of Logarithms
- 3.8. Common and Natural Logarithms
- 3.9. Exponential Models
- 3.10. Logarithmic Models
- 3.11. Simple and Compound Interest
- 3.12. Exponential Decay
- 3.13. Exponential Growth

### Chapter Summary

## Summary

Introduction to the algebraic and geometric views of exponential and logarithmic functions. Calculation and graphing methods of analyzing both types of functions are covered.

Descriptions and applications of exponential and logarithmic growth and decay are discussed, as is the difference between exponential and logarithmic functions.

Students will learn to convert to logs from exponents and back, and will learn to expand and condense logs.

Each lesson includes an embedded video introducing the topic, 3 walkthrough examples, guided practice, and a number of practice problems.