Lesson Plan: Modeling with Exponential and Logarithmic Functions
Created fall 2014 by Christie Marie Ginson, Guam Community College
Lesson Overview
Unit
Subject
Exponential and Logarithmic Functions
Finite Mathematics
Lesson Description Write exponential functions to model and solve real-world problems such as
growth of money at compound interest, growth of populations and
radioactive decay. We will also use properties of its inverse, the logarithmic
function to solve exponential equations.
Goals
Lesson Goals
1. The students will be able to graph and identify the properties of
exponential functions and evaluate exponential expressions.
2. The students will be able to use exponential functions to model real life
situations such as the growth of money at compound interest, the growth of
populations and determining the age of a fossil using the concept of
radioactive decay.
Methods
Anticipatory Set
Show students a coral fossil to be passed around in the classroom (or a bone
believed to have been uncovered from an archaeological site). Ask if anyone
could possibly guess the age of this fossil or bone. A set of questions to be
posted to the class are: How long ago did the living organism live? How do
you think archaeologists, when studying ancient fossils, determine how old
their discoveries are? Have you ever heard of a technique called carbon
dating?
Discuss how to write an exponential function to model this real-life situation
and how it is used together with the concept of radioactive decay in
determining the age of a fossil.
Introduce and
Model New
Knowledge

Explain that the mathematical model for exponential growth or decay
is given by
f (t) = A0ekt or A = A0ekt.
If k > 0, the function models the amount or size of a growing
entity.
A0 is the original amount or size of the growing entity at time t = 0.
A is the amount at time t, and k is a constant representing the growth
rate.
If k < 0, the function models the amount or size of a decaying
entity.
A0 is the original amount or size of the decaying entity at time t = 0.
A is the amount at time t, and k is a constant representing the decay
rate.
Provide Guided
Practice
Provide
Independent
Practice

We then use a series of examples to further explain. Please see the
attached Powerpoint presentation.
•
Provide students with practice problems where they must write
exponential functions to model problems in finance, population
growth or archaeology. Students may benefit from working in pairs
to solve these problems.
Assign homework from text. Direct students to use their MathXL web
service where a set of practice problems have been provided for them with
available help tools if they need guidance in solving problems step-by-step
as well as videos showing detailed solutions.
Assessment
Formative/Ongoing
Assessment


Quizzes to assess learning of the exponential functions
Assign students in teams of two or three students. Each team chooses
a specific application problem from the text or other resources, works
on finding the exponential function to model the situation and to
present their detailed solution to the class.
Summative/End of
Lesson Assessment

Unit test
Materials
Handouts for notes, a sample fossil or bone
Course textbook and graphing calculator
Computer and digital projector for the Power point presentation
References:
1. NPETE Presentations at the Summer Indigenous Fellows Institute in Fort Berthold
Community College, North Dakota, July 21-25, 2014
2. www.westga.edu/~srivera/ca-fall05/3.4.ppt
3. http://pubs.usgs.gov/bul/1071f/report.pdf, page 6
4. Macrofossils and Stratigraphic Subdivisions of the Bakken Formation (Devonian –
Mississippian), Williston Basin, North Dakota by Larry C. Thrasher, U.S. Bureau of Land
Management
http://archives.datapages.com/data/sgs_wb_utf/data/0005/0053/0053.html
5. Finite Mathematics for Business, Economics, Life Sciences and Social Sciences, 12th Edition,
Barnett, Ziegler, Byleen, Prentice Hall 2011