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Exponential Functions in Precalculus

Description: 

We will explore exponential functions through graphing and describe the relationship to the compound interest formula.

Learning Targets: 
Graph exponential functions and identify the domain, range, and asymptotes of the function
Solve real-world problems with exponential models and graph exponential models
Interpret exponential models in terms of context
Compute interest when it is compounded continuously and understand the context of continuously compounded interest
Evaluate, compare, and explain results when using the continuously compounded interest formula and justify with logic and reasoning
Link: 
Exponential Functions
https://docs.google.com/document/d/1Qt1wf0-YAKfxZ9P3HYiqioDufXyqYy2gyik8535k-aE/pub
Author: 
wippelkm
Content Area: 
Mathematics
Pre-Calc and Calculus
Language: 
English
Resource Type: 
Lesson
Grade: 
9-12
Common Core Math
Tags: 
exponential
Exponential Function
compound interest
Asymptote
Precalculus
Algebra 2

Student prerequisite skills and knowledge

Students will need a basic knowledge of exponential functions.

What concepts or procedures are being explained or demonstrated in this lesson object?

Procedure/Activities:

For both lessons on this section, I will lead the class in filling out their given note-guides that I created to accompany this section in order to meet the given objectives and cover the selected Common Core benchmarks.  Day 1 of the lesson will focus on sketching graphs for exponential functions while identifying the domain, range, and asymptotes of the function, as well as using exponential models to interpret and make predictions involving real-life phenomena.  We will also graph these models and discuss importance of units, initial velocity, and terminal velocity.  I will also model how to use mental math techniques as an alternative to using their calculator in certain instances.  On Day 2, our focus will be on the continuously compounded interest formula.  We will evaluate and compare results using the continuously compounded interest formula.  We will also draw conclusions from our calculations and write an analysis for our conclusions; discussions on how to enhance our writing about mathematics skills will take place.

Here are the completed Note-Guides: 4.2 Day 1 and 4.2 Day 2

(The blank note-guides for your students are under the materials section!)

Lesson Conclusion/Summary:

At the end of the second day of the lesson, students will complete a formative assessment through Google Forms (they will access this through Google Classroom).  They will either access this on their own devices, or if the Chromebook cart is available, we will use the Chromebooks. This formative assessment will cover exponential functions and the natural exponential function.  I will incorporate a variety of questions including short answer, multiple choice, and select all that apply.

Assessment: Formative /Summative

Google Form (formative--exit slip on day 2 of the section as described above)

Quiz over sections 4.1-4.2 (summative--administered the following day and will cover the given objectives)

Follow-Up Lesson(s):

The next day, we will follow up this lesson with a quiz over graphing exponential functions and the natural exponential function and identifying the domain, range, and asymptotes of these functions, as well as the practical applications of these functions which include evaluating and solving for values involving the compound interest formulas and logistic growth models.  

What was your experience, both successes and challenges, using this lesson object with your students?

Although this lesson was used in my precalculus class, there are also applications for Algebra 2, as well.  The students did very well with the Google Forms.  I love using this because we can see the data of all the answers.  I used the data from the Google Form to go over the misconceptions that the students had in class.  It was a quick way to see everyone’s response and address the incorrect answers with the entire class without “calling-out” a single student.