Module 5: Exponents and Exponential Functions
Module Overview: In this module students will explore different situations that can be modeled with exponential functions and equations. Students
use tables and graphs to contrast the repeated multiplication of exponential patterns with the repeated addition of linear patterns. This unit also
deepens students’ understanding of functions and their notation. Students will investigate key features, domains and ranges of exponential functions;
write exponential functions to model relationships between two quantities as in; and compare properties of exponential functions.
Essential Question:
 How can very large and very small numbers be represented?
 How can expressions with exponents be simplified?
 What is an example of a real world situation that is represented by an exponential function?
 What are the characteristics of exponential functions?
Prerequisite Skills and Knowledge: simplifying expressions with exponents using laws of exponents
Tier III Vocabulary:
Scientific Notation, exponential functions, exponential growth, growth factor, compound interest, exponential decay, decay factor
Common Core Standards for Mathematical Practices
Key
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
 ★ Modeling Standard
 *indicates a standard that appears in multiple modules
 + indicates a standard included to increase coherence
 PH Prentice Hall Algebra One textbook 2011
 BOLD indicates TN Common Core focus standards
abc indicates a part of a standard that appears in a different module
Common Core State Standards for Math Content
N-RN Number-Real Numbers
N-RN.1 Explain how the definition of the meaning of
rational exponents follows from extending the properties
of integer exponents to those values, allowing for a
notation for radicals in terms of rational exponents. For
example, we define 51/3 to be the cube root of 5 because
Students will be able to
Activities/Resources
 Use laws of exponents learned in middle
school to simplify basic expressions that
contain exponents.
(Understanding notation for radicals
in terms of rational exponents will be
addressed in Algebra II.)
Rational Exponents
http://www.mathsisfun.com/
algebra/exponentfractional.html
Cumberland County Algebra One Curriculum Guide 1
we want (5 1/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5.

For school year 2013-14, include
instruction that reviews the eighth grade
content: Scientific Notation and
Operations with Scientific Notation.
A-CED Creating Equations
A. Create equations that describe numbers or
relationships.
A-CED.A.1 Create equations and inequalities in one
variable and use them to solve problems. Include
equations arising from linear and quadratic
functions, and simple rational and exponential
functions.*
 Create and solve exponential functions
from context or data.
 Determine viable and non-viable
solutions in the context of the problem.
http://www.gvsd.org/cms/li
b02/PA01001045/Centricit
y/Domain/446/A1TE1008.
pdf
A-CED.A.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.*
F-LE Functions-Linear, Quadratic, and Exponential
Models 
A. Construct and compare linear, quadratic, and
exponential models and solve problems.
Comparing Linear data to
exponential data/quadratic
data
http://www.virtualnerd.co
m/common-core/hsffunctions/HSF-LE-linearquadratic-exponentialmodels
Create exponential functions given geometric
sequences.
Comparing Functions
Task
http://www.insidemathemati
cs.org/common-core-mathtasks/high-school/HS-F2008%20Functions.pdf
F-LE.A.2 Construct linear and exponential functions,
including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two input-output
pairs (including these from a table).
Cumberland County Algebra One Curriculum Guide 2
F-LE Linear, Quadratic, and Exponential Models

Show that linear functions change at the
same rate over time and that exponential
functions change by equal factors over
time.

Describe situations where a quantity
grows or decays at a constant percent
rate per unit interval as compared to
another.

Use graphs and tables to show that a
quantity that is increasing exponentially
will eventually exceed the same
quantity increasing linearly,
quadratically, or by any other
polynomial function.

Based on the context of a situation,
explain the meaning of the coefficients,
factors, exponents, and/or intercepts of
an exponential function.
A. Construct and compare linear, quadratic, and
exponential models and solve problems.
F-LE.A.1 Distinguish between situations that can be
modeled with linear functions and with exponential
functions.
a. Prove that linear functions grow by equal differences
over equal intervals, and that exponential functions
grow by equal factors over equal intervals.
c. Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval
relative to another.
F-LE.A.3 Observe using graphs and tables that a
quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more
generally) as a polynomial function.
B. Interpret expressions for functions in terms of the
situation they model.
F-LE.B.5 Interpret the parameters in a linear or
exponential function in terms of context.
Cumberland County Algebra One Curriculum Guide 3
A-SSE Algebra- Seeing Structure in Expressions

Use properties of exponents (such as
power of a power, product of powers,
power of a product, etc.) to write an
equivalent form of an exponential
function to reveal and explain specific
information about its approximate rate
of growth or decay.

Graph exponential functions that arise
from conceptual situations.

Describe intercepts and end behavior of
exponential functions.

Determine domain and range of
exponential functions.

Compare the key features of two
exponential functions each represented
a different way.
B. Write expressions in equivalent forms to solve
problems.
A-SSE.B.3 Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression. ★
Spread of Disease
http://www.achieve.org/files/CC
SS-CTE-Spread-of-DiseaseFINAL.pdf
Use the properties of exponents to transform expressions
for exponential functions. For example the expression
1.15t can be rewritten as (1.151/12)12t  1.012 to reveal
the approximate equivalent monthly interest rate if the
annual rate is 15%.
12t
PF-IF Functions-Interpreting Functions
C. Analyze functions using different representations.
F-IF.C.7 Graph functions expressed symbolically and
show key features of the graph, by hand in simple cases
and using technology for more complicated cases. ★
F-IF.C.9 Compare properties of two functions each
represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For
example given a graph of one exponential function and
an algebraic expression for another say which one will
reach a certain value first.
Functions Task (covers a
variety of this units standards
and has several tasks listed for
the entire unit)
https://www.georgiastandards.org
/CommonCore/Common%20Core%20Fram
eworks/CCGPS_Math_912_AccelCoorAlgebraAnalyticGe
om_Unit3SE.pdf
Cumberland County Algebra One Curriculum Guide 4
S-ID Interpreting Categorical and Quantitative Data

B. Summarize, represent, and interpret data on two
categorical and quantitative variables.

S-ID.B.6 Represent data on two quantitative variables on
a scatter plot, and describe how the variables are related.
a.
Fit a function to the data: use functions fitted to
data to solve problems in the context of the data.
Use given functions or choose a function suggested
by the context. Emphasize linear, quadratic, and
exponential models.*


Create a scatter plot from two
quantitative variables.
Categorize data as exponential or not.
Use algebraic methods and technology
to fit an exponential function to the
data. Use the function to predict values.
Explain the meaning of the growth rate
and y-intercept in context.
Explain the meaning of the constant and
coefficients in context.
Cumberland County Algebra One Curriculum Guide 5