7.1 & 7.2 - Graphing Exponential Transformations Do NOW Exponential Equation: f(x) = Cax C: COEFFICIENT a: BASE X: EXPONENT Exponential Equations Graph is above the x-axis Domain: (–∞, ∞); Range: (0, ∞) Exponential Growth When the base is greater than 1, a > 1 f(x) is INCREASING Exponential Decay When the base is between zero and one, 0 < a < 1 f(x) is DECREASING 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Worksheet Key Exponential Equation: f(x) = Cax C: COEFFICIENT a: BASE X: EXPONENT Exponential Equations Graph is above the x-axis Domain: (–∞, ∞); Range: (0, ∞) Exponential Growth When the base is greater than 1, a > 1 f(x) is INCREASING Exponential Decay When the base is between zero and one, 0 < a < 1 f(x) is DECREASING 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

Graphing Exponential Functions Section 7.1 and 7.2, Revised ©2013, vdang@houstonisd.org 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Review Linear Quadratic Algebraically Equation: 9x + 3y = –6 Equation: y = 5x2 – 7x + 3 Verbally Line Parabola Table Common Difference Common Ratio Graph x 1 2 3 y 4 9 x 1 2 3 y 16 8 4 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

Growth vs Decay Algebraically Verbally Table Graph Exp. Growth Exp. Decay Algebraically Verbally Increases by the same rate in each time period Examples: Population, Compound Interest, Cell Growth, and Bacteria Decreases by the same rate in each time period Examples: Investment Loss, Evaporation, Depreciation Table X increases, Y increases X increases, Y decreases Graph Algebraically Equation: y = c • (1 + r)x c: Initial Value r: Percentage x: Time Period y = c • (1 – r)x x 1 2 3 y 4 8 16 x 1 2 3 y 16 8 4 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 1 Determine whether represents exponential growth or decay. 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 2 Determine whether represents exponential growth or decay. 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Your Turn Determine whether represents exponential growth or decay. 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

Graphing Exponentials Make a table of values, usually from [–3, 3] Plot the points from the table Connect the dots and draw from left to right, a smooth curve and label any asymptotes 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 3 Graph f(x) = 2x x f(x) –3 (2)–3 1/8 –2 (2)–2 1/4 –1 (2)–1 1/2 (2)0 1 (2)1 2 (2)2 4 3 (2)3 8 x f(x) –3 (2)–3 –2 (2)–2 –1 (2)–1 (2)0 1 (2)1 2 (2)2 3 (2)3 x f(x) –3 –2 –1 1 2 3 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 3 Graph f(x) = 2x x f(x) –3 (2)–3 1/8 –2 (2)–2 1/4 –1 (2)–1 1/2 (2)0 1 (2)1 2 (2)2 4 3 (2)3 8 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 3 Graph f(x) = 2x (Calculator check) 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 4 Graph f(x) = (1/2)x x f(x) –3 (1/2)–3 8 –2 (1/2)–2 4 –1 (1/2)–1 2 (1/2)0 1 (1/2)1 1/2 (1/2)2 1/4 3 (1/2)3 1/8 x f(x) –3 (1/2)–3 –2 (1/2)–2 –1 (1/2)–1 (1/2)0 1 (1/2)1 2 (1/2)2 3 (1/2)3 x f(x) –3 –2 –1 1 2 3 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 4 Graph f(x) = (1/2)x x f(x) –3 (1/2)–3 8 –2 (1/2)–2 4 –1 (1/2)–1 2 (1/2)0 1 (1/2)1 1/2 (1/2)2 1/4 3 (1/2)3 1/8 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 5 Graph f(x) = 3(2/3)x (decimals are acceptable) x f(x) –3 –2 –1 1 2 3 –3 3(2/3)–3 10.125 –2 3(2/3)–2 6.75 –1 3(2/3)–1 4.5 3(2/3)0 3 1 3(2/3)1 2 3(2/3)2 5/3 3(2/3)3 .889 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Your Turn Graph f(x) = 1/2(2)x (decimals are acceptable) x f(x) –3 –2 –1 1 2 3 –3 1/2(2)–3 0.0625 –2 1/2(2)–2 .125 –1 1/2(2)–1 .25 1/2(2)0 0.5 1 1/2(2)1 2 1/2(2)2 3 1/2(2)3 4 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

Exponential Growth/Decay Formula Equation, y = a(1 + r)t a = Initial Amount r = Interest Rate + = Growth/Decay Rate t = time 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 6 The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a function that models the value of the car over time. Then, determine the value of the car in 2004. C = ?? A = 11,000 R = 0.069 T = t C = A = R = T = 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 6 The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a function that models the value of the car over time. Then, determine the value of the car in 2004. C = ?? A = 11,000 R = 0.069 T = 20 C = A = R = T = 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Example 7 You put $350 into a savings account that earns 3% annual interest compounded yearly. How much will your investment be worth in 4 years? C = ?? A = 350 R = 0.03 T = 4 C = A = R = T = 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Your Turn The owner of an original copy of a 1938 comic book sold it at an auction in 2005. The owner bought the comic book for $55 in 1980. The value of the comic book increased at a rate of 2.8% per year. Write a function and determine the approximate value in 2008. 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations

7.1 & 7.2 - Graphing Exponential Transformations Assignment Worksheet 12/8/2018 11:20 AM 7.1 & 7.2 - Graphing Exponential Transformations