# Ch 5: On Core Mathematics Algebra 1 Unit 5: Exponential Functions

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Exponential Functions chapter of your textbook.
- Watch fun videos that cover the exponential functions concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Definition of an exponential function
- Exponential growth vs. decay
- Definition of a logarithm
- Writing and graphing exponential functions
- Solving exponential equations
- Exponential and logarithmic regressions
- Comparing linear and exponential functions
- Modeling both types of functions

*On Core Mathematics is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. What Is an Exponential Function?

Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!

### 2. Exponential Growth vs. Decay

How is it that it only takes four years for our computer to go from top-of-the-line to almost worthless? Well, it has something to do with what's called exponential decay, which we'll learn about here!

### 3. What is a Logarithm?

Logarithms can help you solve exponential functions. In this lesson, you will learn about how to work with and recognize logarithms, and how to use logarithm notation with an example problem about earthquakes!

### 4. Writing & Graphing Exponential Functions

In this lesson, we will explore exponential functions and their properties. Through real world examples and explanation, we will see how to write and graph these types of functions.

### 5. How to Solve Exponential Equations

Read this lesson to learn the steps you need to take to solve exponential equations. You'll see that it's not too difficult; you just need to make use of one other mathematical operation in order to solve your problems.

### 6. Comparing Linear & Exponential Functions

In this lesson, we will go over the definition of linear and exponential functions then compare and contrast the two. We will talk about how to decide if a function is linear or exponential and go over examples of each.

### 7. Modeling with Exponential & Logarithmic Functions

This lesson will give a quick review of exponential and logarithmic functions and when to use these functions to model data. Then we will explore the use of graphing calculators in finding exponential and logarithmic functions to model given data.

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### Other Chapters

Other chapters within the Harcourt On Core Mathematics - Algebra 1: Online Textbook Help course

- On Core Mathematics Algebra 1 Unit 1: Algebraic Modeling and Unit Analysis
- On Core Mathematics Algebra 1 Unit 2: Linear Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 3: Systems of Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 4: Linear Functions
- On Core Mathematics Algebra 1 Unit 6: Piecewise and Absolute Value Functions
- On Core Mathematics Algebra 1 Unit 7: Quadratic Functions of the Form of f(x) = a(x-h)^2 + k
- On Core Mathematics Algebra 1 Unit 8: Quadratic Functions of the Form of f(x) = ax^2 + bx + c
- On Core Mathematics Algebra 1 Unit 9: Data Analysis