1. "Insanity: doing the same thing over and over again and expecting different results." ~~ Albert Einstein LevelPowerNumber of Pliers Value Original2020 11 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

2. 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?

3. 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

4. CFU3102.3.34; Graph exponential functions in the form y = a(bx) where b ≠ 0. CLE 3102.3.6; Understand and use relations and functions in various representations to solve contextual problems.; SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation; SPI 3102.1.1; Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation; SPI 3102.1.2; Write an equation symbolically to express a contextual problem; SPI 3102.1.4 Translate between representations of functions that depict real-world situations; SPI 3102.1.5; Recognize and express the effect of changing constants and/or coefficients in problem solving.; SPI 3102.3.6; Interpret various relations in multiple representations.: SPI 3102.3.7; 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 3102.5.1; 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 3102.5.3 Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.

5. "Insanity: doing the same thing over and over again and expecting different results." ~~ Albert Einstein LevelPowerValue Original2020 1 First2121 2 Second2 4 Third2323 8 Fourth2424 16 Fifth2525 32 Sixth2626 64 Seventh2727 128 Eighth2828 256 y= a x y= 2 x Exponential Function Where did we see this? LevelPowerValue Original2020 First2121 Second2 Third2323 Fourth2424 Fifth2525 Sixth2626 Seventh2727 Eighth2828

6. Powe r PlierValue 2020 2(1)11 2 -1 1/2 1 ½0.5 2 -2 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 Powe r PlierValue 2020 2(1)11 2 -1 1/2 1 ½0.5 2 -2 1/2 2 ¼0.25 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 Powe r PlierValue 2020 2(1)11 2 -1 1/2 1 ½0.5 2 -2 1/2 2 ¼0.25 2 -3 1/2 3 1/80.125 2 -4 2 -5 2 -6 2 -7 2 -8 PowerPlierValue 2020 2(1)11 2 -1 1/2 1 ½0.5 2 -2 1/2 2 ¼0.25 2 -3 1/2 3 1/80.125 2 -4 1/2 4 1/160.0625 2 -5 2 -6 2 -7 2 -8 PowerPlierValue 2020 2(1)11 2 -1 1/2 1 ½0.5 2 -2 1/2 2 ¼0.25 2 -3 1/2 3 1/80.125 2 -4 1/2 4 1/160.0625 2 -5 1/2 5 1/320.0313 2 -6 1/2 6 1/640.0156 2 -7 1/2 7 1/1280.0078 2 -8 1/2 8 1/2560.0039 Domain of this Function? All Real Numbers Range of this Function? Y > 0 (all positive #) Y intercept? X = 0, Y = 1

7. 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

8. Function 0<a<1 y= ( ½ ) x x( ½ ) x y -3( ½ ) -3 (2) 3 = 8 -2 01 1 2 x( ½ ) x y -3( ½ ) -3 (2) 3 = 8 -2( ½ ) -2 4 ( ½ ) -1 2 011 1( 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

9. Power2x2x 2 x +2 2525 32 2424 16 2323 8 2 4 2121 2 2020 1 2 -1 0.5 2 -2 0.25 2 -4 0.0625 2 -8 0.0039 Power2x2x 2 x +2 2525 3234 2424 1618 2323 810 2 46 2121 24 2020 13 2 -1 0.52.5 2 -2 0.252.25 2 -4 0.06252.065 2 -8 0.00392.039 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

10. 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(0.82 1 ) Value = $20, 500 Y 1 = 25000*0.82^x

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

12. +6+6 +6+6 +6+6 +6+6 +6+6 No Can you multiply or divide Y by the same number each time?

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