Exponential functions in
the Real World
Name:
Monica Sustaita
Title
of lesson: Exponential
functions in the Real World
Date
of lesson: Thursday, Week 4
Length
of lesson: 12
days
Description of the class:
Name of course: Algebra I
Grade level: 8^{th} or 9^{th}
grade
Honors or regular: Regular
Source of the lesson:
Miranda
and the Rookie
http://mathforum.org/tpow/print_puzzler.ehtml?puzzle=207
TEKS
addressed:
(a) Basic
understandings
(4)
Relationship between equations and functions. Equations arise as a way of
asking and answering questions involving functional relationships. Students
work in many situations to set up equations and use a variety of methods to
solve these equations.
(5) Tools
for algebraic thinking. Techniques for working with functions and equations are
essential in understanding underlying relationships. Students use a variety of
representations (concrete, numerical, algorithmic, graphical), tools, and technology, including,
but not limited to, powerful and accessible handheld calculators and computers
with graphing capabilities and model mathematical situations to solve
meaningful problems.
(d)
Quadratic and other nonlinear functions: knowledge and skills and performance
descriptions.
3) The
student understands there are situations modeled by functions that are neither
linear nor quadratic and models the situations. Following are performance
descriptions.
(A) The
student uses patterns to generate the laws of exponents and applies them in
problemsolving situations.
(B) The
student analyzes data and represents situations involving inverse variation
using concrete models, tables, graphs, or algebraic methods.
(C) The
student analyzes data and represents situations involving exponential growth
and decay using concrete models, tables, graphs, or algebraic methods
I.
Overview
In this lesson, students
will get to see how an exponential function works in the real world. It is important because they can see how real
life situations can be modeled by functions.
II. Performance or learner outcomes
Students
will be able to:
á
Describe the effects of exponential functions
III. Resources, materials and supplies needed
á
Computer per group
á
Microsoft Excel
IV. Supplementary materials, handouts.
á
Handout and questions
FiveE
Organization
Teacher Does Probing Questions Student
Does
Engage: Talk a little about money and
give an initial situation. Explain the question. 
So, which salary would you take right now, MirandaÕs or the rookieÕs? Why? 
Thinking a million dollars is
going to be way more than double the amount from year to year, they choose MirandaÕs. 
Explore: Handout the problem and divide the students into groups. Walks around, monitoring the
progress of the groups. Shows them how to make a
graph using Excel. 
Describe the graphs in your group. 
Students break into groups
and get into Excel. Enter the data into Excel
giving titles where needed. See and compare the graphs. 
Explain: As a class, we come together and answer the questions. 
What
is MirandaÕs salary in year 15? What is the rookieÕs? In
which year does the rookieÕs salary overtake MirandaÕs? At
the end of 25 years, who received the most money? What
is MirandaÕs salary in year n? What is the rookieÕs? What is MirandaÕs
total at n years? RookieÕs? 
Read and explain their
answers. 15, 000,000 16,384 In year 21. The rookie M=1,000,000 R=2^n m=1,000,000n r=· _{i}_{=1}^{n }2^{n} (they would be able to write this but they
should be able to explain it comparing to how they got MirandaÕs
total) 
Extend / Elaborate: Teacher asks other questions not on
paper. 
So, now whose salary would
you pick? What if you only planned to play 10 years? 20 years?
30 years? Why? What kind of function does
MirandaÕs salary represent? The rookieÕs? What is a general
statement that you can make about exponential and constant functions? 
The RookieÕs. MirandaÕs. MirandaÕs. The RookieÕs? Constant. Exponential. 
Evaluate: Give other problems using that same
kind of scenario. Have the groups do each of their assigned problems and then present and explain them. 

Students
work on the problems and present to the class. 
Percent
effort each team member contributed to this lesson plan:
___%___ ____Name of group
member_____________________
___%___ ____Name of group
member_____________________
Name_________________________
Miranda and the Rookie
Miracle Miranda plays for the
California Hoops basketball team. After the Hoops won the WNBA championship,
the manager offered her a million dollars a year for the next 25 years,
whereas a new rookie for the same team was given $1 the first year, $2 the
second year, $4 the third year, and so on, for the next 25 years. 

1.
What is Miranda's salary in year 15? What is the rookie's?
2.
In which year does the rookie's salary overtake Miranda's?
3.
At the end of 25 years, who has received the most money?
4. What is Miranda's salary in year n? What is the rookie's?