About This Chapter
Below is a sample breakdown of the Exponential Functions & Logarithmic Functions chapter over the course of 14 school days. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Exponential functions||Definition of exponential functions|
|Tuesday||Exponential growth vs. decay||How to assess exponential growth versus decay|
|Wednesday||Transformation of exponential functions||How to horizontally and vertically translate an exponential function|
|Thursday||Natural base e||Definition of the natural base and how to graph natural base functions|
|Friday||Logarithms||Definition and evaluation of logarithms|
|Monday||Inverse of logarithmic functions||How to rewrite logarithmic equations in exponential form and the other way around|
|Tuesday||Exponentials, logarithms and the natural log||Definition and functionality of exponentials, logarithms and the natural log|
|Wednesday||Basic and shifted graphs of logarithmic functions||Graphing a logarithmic function and identify the domain, range and vertical asymptote|
|Thursday||Properties of logarithms||Definitions of logarithmic properties and practice problems|
|Friday||Solving logarithmic equations||Steps and rules for solving logarithmic equations|
|Monday||Change-of-base formula||Definition of the change-of-base-formula and how to apply it to evaluate logarithmic expressions|
|Tuesday||Solving exponential equations||Steps and rules for solving exponential equations|
|Wednesday||Rate and exponential growth||The population dynamics problem|
|Thursday||Exponential and logarithmic function behavior||Large-scale behaviors of exponential and logarithmic functions|
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. Transformation of Exponential Functions: Examples & Summary
All exponential functions follow a basic graph. But when you make changes to the function, you will see the graph shift and make changes. Watch this video lesson to learn how to easily identify these changes or transformations.
4. Using the Natural Base e: Definition & Overview
In this video lesson, you will learn what kind of number 'e' is. Also learn the formal name for this unique number. See what kind of graph the natural base 'e' graphs into, as well as the uses of these types of functions.
5. 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!
6. How to Evaluate Logarithms
Using this lesson, you can get practice evaluating logarithms, as well as learn some of the shortcuts behind writing and estimating them. You can also learn how to use your calculator to evaluate logarithms, and learn about a concept called the change of base theory.
7. Writing the Inverse of Logarithmic Functions
Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.
8. Exponentials, Logarithms & the Natural Log
Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.
9. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples
Watch this video lesson and you will see what the basic graph of the logarithmic function looks like. You will also be able to identify the kind of shifts that will occur by just looking at a logarithmic function when you finish the video.
10. Logarithmic Properties
Along with the change of base property, there are three other logarithmic properties that allow you to manipulate expressions to your advantage. Learn about the product rule, quotient rule and power rule here.
11. Practice Problems for Logarithmic Properties
As you get further and further into mathematics, logarithms will appear more and more. It's the point of this lesson to get you used to dealing with them and able to know what to do when you see a whole line of paper full of them!
12. How to Solve Logarithmic Equations
If you're ever picking out a telescope to see your favorite planet, make sure you do the math first! Learn how to solve the logarithmic equation that will get you the size telescope you want.
13. Using the Change-of-Base Formula for Logarithms: Definition & Example
Logarithms have many uses in the real world. But what happens when the calculation uses a base other than the standard base 10? Watch this video to find out how to handle this situation and the formula to use.
14. 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.
15. Calculating Rate and Exponential Growth: The Population Dynamics Problem
You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.
16. Behavior of Exponential and Logarithmic Functions
After watching this video lesson, you will be able to recognize exponential and logarithmic functions by looking at the end behavior of the graphs. You will also learn how the graphs change.
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Other chapters within the Trigonometry Curriculum Resource & Lesson Plans course
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