Unit Target: Exponential functions
A1.1.A
A1.1.E
A1.2.C
Select and justify functions and equations to model and solve problems.
Solve problems that can be represented by exponential functions and equations.
Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify
and evaluate exponential expressions.
A1.3.A Determine wheather a relationship is a function and identify the domain, range, roots, and independent and dependent
variables
A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these
representations.
A1.7.A Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in
the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
A1.7.B Find and approximate solutions to exponential equations.
Target
 I can simplify an algebraic
expression with negative
coefficients, rational exponents,
and write the square root of a
non-perfect square in simplest
radical form
4
 I can use algebra to solve
exponential equations of the
x
form y = ab , for x
 I can identify the domain/range
of an exponential function when
given a contextual situation that
imposes restrictions
Examples
Simplify the following:
3 4 -3
(-2x y )
27
4
3
48
Solve y = 4(3x ) for x algebraically.
A bank will give you a 5 year loan on $1500 for a dirt bike. What is the domain and
range of this function?
 I can apply the laws and
properties of exponents to
simplify algebraic and numerical
expressions with integer
exponents
 I can match a graph, table, or
equation to a given context
involving exponential functions
 Given a graph, table, or equation
I can find and approximate
solutions to exponential
functions
3
 I can identify the domain/range
of an exponential function when
given an equation
 I can describe the effects that
changes in the parameters a and
b have on an exponential graph
of the form y = abn , and
compare situations modeled by
exponential functions
æ x2 ö
Simplify ç -3 ÷
èx ø
4
If we start with one bacteria, it can double every hour, which equation represents this
situation?
y = x2
y = 2x
y = 2x
y=
2
x
A pond has 4 water lilies in it that triple every day. This can be represented by the
equation y = 4(3x ) . The pond can only hold 4000 water lilies. How long will it take for
the water lilies to cover the pond?
Given 16 = 4(3x ) determine which two integers the value of x lies between
Given y = 6(5x ) what is the value of x when y is 6?
Identify the domain and range of the function y = 5x
You have won a door prize and are given a choice between two options:
a. $150 invested at 4% compounded annually.
b. $200 invested at 3% compounded annually.
How much is each worth at the end of 10 years?
 I can simplify algebraic
expressions with positive integer
and zero exponents, with a
negative integer base, and write
the cube root of a perfect cube
 I can match a graph or table to
an exponential equation
2
 Given an equation of the form
y = abn , I can evaluate it for
whole number and zero values of
n
 I can identify the domain/range
of an exponential function when
given a table or a set of points
Simplify the following:
(a3b 4 )2
(30 43 x 2 )3
3
216
Which table represents the equation y = 3x
x
0
1
2
3
y
0
1
8
27
x
0
1
2
3
y
1
3
9
27
x
0
1
2
3
y
0
1
4
8
x
0
1
2
3
y
1
3
6
9
Given y = 3(4 x ) , what is the value of y when x is 3?
An exponential function is represented in the table below. What is the domain and
range of the function?
x
0
1
2
3
y
432
144
48
16
 I can simplify numerical
expressions with positive integer
exponents and write the square
root of a perfect square
Simplify the following:
(2334 )2
225
Identify the exponential graph(s).
 I can identify an exponential
equation or exponential graph
 Given an equation of the form
x
y = b , I can evaluate it for
positive integer values of x
1
 I can identify the domain/range
of an exponential function when
given a graph
Vocabulary:
 approximate
 base
 compounded annually (context term)
 cube (exponent)
 cube root
 domain
Given y = 3x what is the value of y when x is 5?
What is the domain and range of the graph below?






exponent (7)
exponential
evaluate
function
initial
integer






law of exponents (8)
power (exponent) (8)
radical
range
simplify
square (exponent)