Unit 5: Exponential and Logarithmic Functions
In this unit students will explore exponential and logarithmic functions. They will understand how exponential functions relate to geometric sequences that they learned in Unit 4 and that exponential and logarithmic functions are inverses of one another.
Prerequisite Units: Unit 4 (not 100% necessary, but helpful)
Materials needed: Computer (Microsoft Excel (5.0) and internet research (5.7), Calculator
Approximately 20 Days needed
Prerequisite Units: Unit 4 (not 100% necessary, but helpful)
Materials needed: Computer (Microsoft Excel (5.0) and internet research (5.7), Calculator
Approximately 20 Days needed
5.0: Unit 5 Introduction
I have my students get in pairs and go through Lesson 5.0 the day after they take their unit test for Unit 4 (Sequences and Series). This is a review of the Excel basics they learned in lesson 4.5 and introduces exponential growth and decay functions as they sort of relate to a geometric sequence. They are encouraged to use Excel or Google Sheets for this exercise. Google Sheets is easier for me as a teacher because they can share their file with me and I can evaluate their work with less clicks on my end. Note that exponential growth and decay functions are continuous and geometric series are discrete  this is is an important distinction to point out to your students.
Lesson 5.0 Word Document

Lesson 5.0 completed Excel File



5.1: Exponential Growth Functions
Lesson 5.1 Smart Notebook File

Lesson 5.1 PDF File


Powerpoint  Compound Interest

Powerpoint  Annual vs. Continuous Compounding

Problem Set 5.1

Problem Set 5.1 Solutions


Lesson 5.1 Video 

Two Good Problems before you move on
The next two problems were taken from Nils' problem sets (found at the bottom of the page). While they are on his original problem sets, I preferred to complete these exercises as in class activities. The problem sets for lessons 5.1 and 5.2 are both editable word documents so they can easily be added into the problem sets if prefer. The "Rule of 70" problem would go with lesson 5.1 and the "Sahara Desert" problem would go with lesson 5.2.
Rule of 70 Problem (PS 7.1#7 on Nils materials below)
Can be added to PS 5.1 
Sahara Desert Problem (PS 7.2#1 on Nils materials below)
Can be added to PS 5.2 


5.2: Exponential Decay Functions
Lesson 5.2 Smart Notebook File

Lesson 5.2 PDF File


Problem Set 5.2

Problem Set 5.2 Solutions


Lesson 5.2 Video 

5.12 Review Worksheet
WORD DOCUMENT 
5.3: Rational Exponents and Radical Expressions (review)
Lesson 5.3 Smart Notebook File

Lesson 5.3 PDF File


Problem Set 5.3

Problem Set 5.3 Solutions


Lesson 5.3 Video 

Exercises before you move to lesson 5.4
Before you do Lesson 5.4 which is evaluating logarithms it is important you do one or both of the following exercises. They are both exploratory, discovery based activities which will help students wrap their mind around what a logarithm actually is. It should be noted that all of my students have already learned what logarithms are in Algebra 2 and close to 100% have negative feelings towards them based on their previous experiences.
Logarithms with Powers of 10 Exploration (need a calculator)
These problems are taken from Phillips Exeter Academy's Problem Based Learning Curriculum

What exactly is a logarithm?
This activity is inspired by Vi Hart's video "How I Feel About Logarithms." I used to have my students simply watch her video, but now I find it more beneficial to carry them through her exploration of what logarithms are. The word document below is the tool I use to help guide students through the contents of the video. Then we watch the video together after the exploration is complete. Like to video is below. https://www.youtube.com/watch?v=N7tcTIrers 
Definition of a Logarithm


5.4: Evaluating Logarithms
Lesson 5.4 Smart Notebook File

Lesson 5.4 PDF


Powerpoint  Relationships between Logarithmic and Exponential Functions
POWERPOINT 
Problem Set 5.4

Problem Set 5.4 Solutions


Lesson 5.4 Video 

5.5: Properties of Logarithms
Lesson 5.5 Smart Notebook File

Lesson 5.5 PDF


Powerpoint  Properties of Logarithms
POWERPOINT 
Problem Set 5.5

Problem Set 5.5 Solutions


Lesson 5.5 Video 

5.6: Solving Exponential and Logarithmic Equations
Lesson 5.6 Smart Notebook File

Lesson 5.6 PDF


Problem Set 5.6

Problem Set 5.6 Answers (not full solutions)



More Practice for 5.6
WORD DOCUMENT 
Lesson 5.6 Video 

5.7: Logarithmic Scales
In the 20182019 school year Jessica used the following lesson which was designed to get students to explore and understand what a Logarithmic Scale is. In the 20192020 school year Jessica will be expanding this lesson to include several of Nils' materails which are outlined and labeled.
Lesson 5.7 Smart Notebook File

Lesson 5.7 PDF

Events in Biological History (a comparison between linear and logarithmic scales

Here is Today Illustration

Powerpoint  Logarithmic Scales

Movie: "Powers of TEN"

Problem Sets titled 7.7 and 7.8 from the additional resources below correlate to the lesson on Logarithmic Scales and Power of TEN Video.

Additional Resources
Problem Sets by Nils Abel  they are labeled Unit 7 in his materials instead of Unit 5

Problem Set Solutions
