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 and Calculator
Approximately 20 Days needed
Prerequisite Units: Unit 4 (not 100% necessary, but helpful)
Materials needed: Computer and 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 Guided Notes (Word) |
| Lesson 5.0 Finished (XLS) |
5.1: Exponential Growth and Decay Functions Introduction
Lesson Resources
Students will need a computer to use Desmos for the investigation in the notes.
| Lesson 5.1 Guided Notes (Word) |
| Lesson 5.1 Guided Notes (PDF) |
| Problem Set 5.1 (Word) |
| Problem Set 5.1 (PDF) |
| Problem Set 5.1 Solutions |
Activities and Extra Resources
The Cocaine Hippos Problem was presented by Mahmoud Harding (NCSSM) at the Teaching Contemporary Mathematics Conference (2022).
| Cocaine Hippos Investigation (Word) |
| Cocaine Hippos Investigation (PDF) |
Exponential Growth Video
|
|
Exponential Decay Video
|
|
5.2: Exponential Growth and Decay Applications
Lesson Resources
| Lesson 5.2 Guided Notes (Word) |
| Lesson 5.2 Guided Notes (PDF) |
| Problem Set 5.2 (Word) |
| Problem Set 5.2 (PDF) |
Activities and Extra Resources
| Rule of 70 Problem |
| Sahara Desert Problem |
| Compound Interest (PPT) |
| Annual vs. Continuous Compounding (PPT) |
| 5.1 - 2 Review Worksheet (Word) |
CO2 Concentration Mauna Loa, HI CODAP File
CO2 concentration Mauna Loa, HI Solutions
Coffee Cool Data CODAP File
Coffee Cool Data Solutions
CO2 concentration Mauna Loa, HI Solutions
Coffee Cool Data CODAP File
Coffee Cool Data Solutions
5.3: Rational Exponents and Radical Expressions (review)
Lesson Resources
Typically I will do a formative assessment after lesson 5.2 and assign the video below as a homework assignment that evening. We do Problem Set 5.3 and the Lesson 5.4 Introduction activity in the following class.
| Lesson 5.3 Guided Notes (PDF) |
| Problem Set 5.3 (Word) |
| Problem Set 5.3 (PDF) |
| Problem Set 5.3 Solutions |
Lesson 5.3 Video |
|
Lesson 5.4 Introduction (What is a Logarithm?)
|
Lesson Resources
|
How I feel about Logarithms Video by Vihart Link
The Lesson 5.4 Intro activity is inspired by the video by Vihart linked above. It is basically going through her process more slowly to give students an opportunity to digest the idea of of a logarithm. | ||||
5.4: Evaluating Logarithms
Lesson Resources
| Lesson 5.4 Guided Notes (Word) |
| Lesson 5.4 Guided Notes (PDF) |
| Problem Set 5.4 (Word) |
| Problem Set 5.4 (PDF) |
| Problem Set 5.4 Solutions |
Activities and Extra Resources
| Relationship between Logarithmic and Exponential Functions (PPT) |
Lesson 5.4 Video
|
|
5.5: Properties of Logarithms
Lesson Resources
| Lesson 5.5 Guided Notes (Word) |
| Lesson 5.5 Guided Notes (PDF) |
| Problem Set 5.5 (Word) |
| Problem Set 5.5 (PDF) |
| Problem Set 5.5 Solutions |
Activities and Extra Resources
| Properties of Logarithms (PPT) |
Lesson 5.5 Video
|
|
5.6: Solving Exponential and Logarithmic Equations
Lesson 5.6 Smart Notebook File
| Lesson 5.6 Guided Notes (Word) |
| Lesson 5.6 Guided Notes (PDF) |
| Problem Set 5.6 (Word) |
| Problem Set 5.6 (PDF) |
| Problem Set 5.6 Solutions |
Lesson 5.6 Video
|
|
Murder Mystery Activity
In this activity students will use what they have learned to determine who killed Mr. Boddy. The activity was created by Jenna Ren and can be purchased on Teachers Pay Teachers for $4.50 here. Before the activity I go through Newton's Law of Cooling and Half Life withe the notes below. I put the students in groups and call them detectives. They have two class periods to solve the mystery and put together a presentation for the grand jury.
| Newton's Law of Cooling and Half Life (Word) |
5.7: Logarithmic Scales
Lesson Resources
| Lesson 5.7 Guided Notes (PDF) |
Activities and Extra Resources
| Logarithmic Scales (PPT) |
| Events in Biological History (XLS) |
| 5.7 Check for Understanding (Word) |
| 5.7 Check for Understanding (PDF) |
5.8: Logistical Growth Models
Lesson Resources
| Lesson 5.8 Guided Notes (Word) |
| Lesson 5.8 Guided Notes (PDF) |
| Sunflower Starter (XLS) |
| Sunflower Complete (XLS) |
Additional Activities with Provided Data Sets (Marc Dancer - Deerfield Academy)
| Logistical Growth Data Sets |
| Logistical Growth Data Sets Solutions |
Additional Resources
|
Problem Sets by Nils Ahbel - they are labeled Unit 7 in his materials instead of Unit 5
|
Problem Set Solutions
|
