# Ch 9: Common Core HS Functions - Exponential & Logarithmic Functions

### About This Chapter

**Standard**: Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. (CCSS.Math.Content.HSF-IF.C.8b)

**Standard**: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (CCSS.Math.Content.HSF-LE.A.1a)

**Standard**: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (CCSS.Math.Content.HSF-LE.A.3 )

**Standard**: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. (CCSS.Math.Content.HSF-LE.A.1c)

**Standard**: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. (CCSS.Math.Content.HSF-IF.C.7e)

**Standard**: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)

**Standard**: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. (CCSS.Math.Content.HSF-LE.A.4)

**Standard**: Interpret the parameters in a linear or exponential function in terms of a context. (CCSS.Math.Content.HSF-LE.B.5)

**Standard**: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. (CCSS.Math.Content.HSF-BF.B.5)

## About This Chapter

After your students have a thorough knowledge of exponential and logarithmic functions, they'll be able to name the five main exponent properties and define both a zero and a negative exponent. Knowledge of exponential and logarithmic functions will also allow students to recognize exponential and logarithmic growth patterns and understand exponential decay and growth.

The lesson topics for this standard include:

- Exponential growth's ability to become enormous
- Graphing exponential functions
- Finding an exponential equation from points, graphs or descriptions
- Solving exponential equations using logarithms
- Interpreting to coefficients of an exponential equation in context
- Logarithmic and exponential functions as inverses of each other
- Graphing logarithmic functions

You'll know when students have a good grasp of the standard once they understand logarithmic properties, can solve logarithmic equations and fully understand transformations of the graphs of exponential and log functions. The lessons might be just what your students need to prepare for college and could even be used to help them gain employment in banking, geologic or chemical industries.

### How to Use These Lessons in Your Classroom

Stuck for ways to make exponential and logarithmic functions engaging? Try these tips to get your students interested in the lessons:

#### Give Students Lessons and Quizzes for Homework

Since there are so many lessons for this standard, you might want to think about occasionally giving students some of them for homework along with some practice problems. Take the lesson quiz in class together and go over the homework assignment in class.

#### Use Flashcards for Definitions

Have students use flashcards for lessons that include definitions, such as *How to Define a Zero and Negative Exponent*. Flashcards can also be used for learning the five main exponent properties. Have students create their own flashcards as additional learning tools that can help engage them in the lesson.

#### Group Lessons Together

Lessons that deal with similar subject matter can be grouped together. For example, any lessons that deal with definitions of exponential and logarithmic functions can be grouped together. Lessons that deal with solving equations or practice problems can also be grouped together. Grouping similar lessons together might be able to help students focus better than they normally would.

### 1. What Are the Five Main Exponent Properties?

We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!

### 2. How to Define a Zero and Negative Exponent

The zero and negative exponent properties are two you will use quite a lot in mathematics. The negative exponent property can be confusing, but when you remember a couple fun ideas, you will get it right every time!

### 3. 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!

### 4. 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!

### 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. 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.

### 7. 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!

### 8. 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.

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### Other Chapters

Other chapters within the Common Core Math - Functions: High School Standards course

- Common Core HS Functions - Basics
- Common Core HS Functions - Sequences
- Common Core HS Functions - Graphing
- Common Core HS Functions - Linear Functions
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Trigonometric Functions