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?

Multiply you _______ the Exponents Divide you ________ the Exponents Power to a Power you ________ the Exponents Monomial has _______ term Binomial has ________ terms Trinomial has ________ terms Polynomial has ______ terms To find the degree of a monomial you ____ the exponents To find the degree of a polynomial you use the __________ degree of the monomials. When adding polynomials you add _____ terms When subtracting polynomials you _____________ then add _______ terms. ADD SUBTRACT MULTIPLY ONE TWO THREE > ONE ADD LAREGEST LIKE CHANGE SIGNS LIKE

CFU ; Recognize and extend arithmetic and geometric sequences. CLE ; Use algebraic thinking to analyze and generalize patterns. SPI ; Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions SPI Express a generalization of a pattern in various representations including algebraic and function notation.

½½½½½ YES Can you multiply or divide Y by the same number each time?

No Can you multiply or divide Y by the same number each time?

Sequence Set of numbers in a specific order Terms Common Difference +8  Arithmetic Sequence Numerical Pattern that increases or decreases at a constant rate or value – Common Difference n th term = a 1 +(n-1)d 4 th 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 Answer: The common difference is 8. So, the sequence is arithmetic. 16 – 8 = 824 – 16 = 832 – 24 = 8

Identify Geometric Sequences B. Determine whether the sequence is arithmetic, geometric, or neither. Explain. 64, 48, 36, 27, Answer: The common ratio is, so the sequence is geometric. __ ___ = __ 3 4 ___ = __ 3 4 ___ =

A.arithmetic B.geometric C.neither A. Determine whether the sequence is arithmetic, geometric, or neither. 1, 7, 49, 343,...

Find Terms of Geometric Sequences A. Find the next three terms in the geometric sequence. 1, –8, 64, –512,... 1 –8 64 –512 The common ratio is –8. = –8 __ 1 –8 ___ 64 –8 = –8 ______ – Step 1Find the common ratio. 262,144 × (–8) –32, –512

Find Terms of Geometric Sequences B. Find the next three terms in the geometric sequence. 40, 20, 10, 5, Step 1Find the common ratio. = __ 1 2 ___ = __ 1 2 ___ = __ 1 2 ___ 5 10 The common ratio is. __ 1 2 Answer: The next 3 terms in the sequence are, __ , and. __ 5 8

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, a 1 = 1. Now find the common ratio. 1 –2 4 –8 = –2 ___ –2 1 = –2 ___ 4 –2 = –2 ___ –8 4 a n = a 1 r n – 1 Formula for the nth term a n = 1(–2) n – 1 a 1 = 1 and r = –2 The common ratio is –2. Answer: a n = 1(–2) n – 1

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 = , 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.B. C.D. Practice Page 581, even*