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 How can exponential functions be identified
through tables, graphs, and equations?
 How are the laws of exponents used to simplify and
evaluate algebraic expressions?
 How can exponential functions be used to model
real world data?
 What are geometric sequences and how are they
related to exponential functions?
ADD
 Multiply you _______
the Exponents
 Divide youSUBTRACT
________ the Exponents
MULTIPLY the Exponents
 Power to a Power you ________
ONE
 Monomial has _______
term
 Binomial has ________
terms
TWO
THREE
 Trinomial has ________
terms
> ONE terms
 Polynomial has ______
ADD the exponents
 To find the degree of a monomial you ____
LAREGEST
 To find the degree of a polynomial you use the __________
degree of the monomials.
LIKE terms
 When adding polynomials you add _____
CHANGE SIGNS then
 When subtracting polynomials you _____________
LIKE
add _______
terms.
 CFU3102.3.1; Recognize and extend arithmetic and
geometric sequences.
 CLE 3102.3.1; Use algebraic thinking to analyze and
generalize patterns.
 SPI 3102.2.1; Operate (add, subtract, multiply, divide,
simplify, powers) with radicals and radical expressions
including radicands involving rational numbers and
algebraic expressions
 SPI 3102.3.1 Express a generalization of a pattern in various
representations including algebraic and function notation.
½
½
½
½
Can you multiply or divide Y by the same
number each time?
YES
½
+
6
+
6
+
6
Can you multiply or divide Y by the same
number each time?
No
+
6
+
6
 Sequence Set of numbers in a specific order
Terms
0
8 16 24
32
Common
Difference +8

Arithmetic Sequence
 Numerical Pattern that increases or decreases at a
constant rate or value – Common Difference
nth term = a1+(n-1)d
4th term = 0+(4-1)8 = 24
Identify Geometric Sequences
A. Determine whether the sequence is arithmetic,
geometric, or neither. Explain.
0, 8, 16, 24, 32, ...
0
8
8–0=8
16
24
16 – 8 = 8
24 – 16 = 8
32
32 – 24 = 8
Answer: The common difference is 8. So, the sequence is
arithmetic.
Identify Geometric Sequences
B. Determine whether the sequence is arithmetic,
geometric, or neither. Explain.
64, 48, 36, 27, ...
64
48
__
3
= 4
64
48
___
36
__
3
= 4
48
36
___
27
__
3
= 4
36
27
___
3 , so the sequence is
Answer: The common ratio is __
4
geometric.
A. Determine whether the sequence is arithmetic,
geometric, or neither.
1, 7, 49, 343, ...
A. arithmetic
B. geometric
C. neither
Find Terms of Geometric Sequences
A. Find the next three terms in the geometric
sequence.
1, –8, 64, –512, ...
Step 1
1
Find the common ratio.
–8
64
–512
The common ratio is –8.
__ = –8
–8
1
–512
64
___
–8
4096
× (–8)
= –8
–512
______
64
–32,768
× (–8)
× (–8)
= –8
262,144
Find Terms of Geometric Sequences
B. Find the next three terms in the geometric
sequence.
40, 20, 10, 5, ....
Step 1
40
40
___
20
Find the common ratio.
20
=
10
__
1
10
___
2
20
=
5
5
__
1 ___
2
10
=
__
1
2
1.
The common ratio is __
2
Answer: The next 3 terms in the sequence are
__
5 , and __
5.
4
8
5
,__
2
Find the nth Term of a Geometric Sequence
A. Write an equation for the nth term of the geometric
sequence 1, –2, 4, –8, ... .
The first term of the sequence is 1. So, a1 = 1. Now find the
common ratio.
1
–2
4
–8
The common ratio
is –2.
–2 = –2 ___
4 = –2 ___
–8 = –2
___
1
–2
4
an = a1rn – 1
Formula for the nth term
an = 1(–2)n – 1
Answer: an = 1(–2)n – 1
a1 = 1 and r = –2
Graph a Geometric Sequence
ART A 50-pound ice sculpture is melting at a rate in
which 80% of its weight remains each hour. Draw a
graph to represent how many pounds of the sculpture
is left at each hour.
Compared to each
previous hour, 80% of the
weight remains.
So, r = 0.80.
50, 40, 32, 25.6, 20.48,….
So after 1 hour, the
sculpture weighs 40
pounds,
32 pounds after 2 hours,
25.6 pounds after 3 hours,
and so forth.
SOCCER A soccer tournament begins with 32 teams in
the first round. In each of the following rounds, one
half of the teams are left to compete, until only one
team remains. Draw a graph to represent how many
teams are left to compete in each round.
A.
C.
B.
D.
Practice
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