"Insanity: doing the same thing over and over again and expecting different results." ~~ Albert Einstein LevelPowerNumber of Pliers Value Original First2121 1(2)2 Second2 1(2)(2)4 Third2323 1(2)(2)(2)8 Fourth2424 Fifth2525 Sixth2626 Seventh2727 Eighth2828 Have a calculator available for Class

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 ; Graph exponential functions in the form y = a(bx) where b ≠ 0. CLE ; Understand and use relations and functions in various representations to solve contextual problems.; SPI Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation; SPI ; Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation; SPI ; Write an equation symbolically to express a contextual problem; SPI Translate between representations of functions that depict real-world situations; SPI ; Recognize and express the effect of changing constants and/or coefficients in problem solving.; SPI ; Interpret various relations in multiple representations.: SPI ; Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.; SPI ; Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).; SPI Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.

"Insanity: doing the same thing over and over again and expecting different results." ~~ Albert Einstein LevelPowerValue Original First Second2 4 Third Fourth Fifth Sixth Seventh Eighth y= a x y= 2 x Exponential Function Where did we see this? LevelPowerValue Original2020 First2121 Second2 Third2323 Fourth2424 Fifth2525 Sixth2626 Seventh2727 Eighth2828

Powe r PlierValue (1) /2 1 ½ Powe r PlierValue (1) /2 1 ½ /2 2 ¼ Powe r PlierValue (1) /2 1 ½ /2 2 ¼ /2 3 1/ PowerPlierValue (1) /2 1 ½ /2 2 ¼ /2 3 1/ /2 4 1/ PowerPlierValue (1) /2 1 ½ /2 2 ¼ /2 3 1/ /2 4 1/ /2 5 1/ /2 6 1/ /2 7 1/ /2 8 1/ Domain of this Function? All Real Numbers Range of this Function? Y > 0 (all positive #) Y intercept? X = 0, Y = 1

Function a>1 y= 4 x Domain of this Function? All Real Numbers Range of this Function? Y > 0 (all positive #) Y intercept? X = 0, Y = 1

Function 0<a<1 y= ( ½ ) x x( ½ ) x y -3( ½ ) -3 (2) 3 = x( ½ ) x y -3( ½ ) -3 (2) 3 = 8 -2( ½ ) -2 4 ( ½ ) ( ½ ) 1 ½ 2(½ ) 2 ¼ Domain of this Function? All Real Numbers Range of this Function? Y > 0 (all positive #) Y intercept? X = 0, Y = 1

Power2x2x 2 x Power2x2x 2 x Domain of this Function? All Real Numbers Range of this Function? Y > 0 (all positive #) Y intercept? X = 0, Y = 4 Shifted Curve Up, changed Y intercept

The value of a new car decreases as soon as it is driven off the dealer’s lot. The function V=25,000(0.82 t ) models the depreciation of a new car. Graph the function. What is the value of the car after 1 year? Value = $25,000( ) Value = $20, 500 Y 1 = 25000*0.82^x

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?

Page 570, 10 – 38 Even* Complete problem 10 as exit ticket.