1. Date: Lesson 8.1

4. I can graph exponential growth functions; graph exponential decay functions. Common Core: CC.9-12.F.IF.7e CRS: FUN 501.

5. Topic: Exponential Growth. CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.* CRS FUN 501. Evaluate polynomial functions, expressed in function notation, at integer values

6. Bell Ringer

7. Warm-Up Exercises Evaluate the expression without using a calculator. 5 2 3 2. State the domain and range of the function –y = ( 2 x – )2)2 3. + 4. 1. 5 2 – 3. – 3 4 2 1 +

8. Warm-Up Exercises Evaluate the expression without using a calculator. ANSWER 1 25 ANSWER 40 5 2 3 2. ANSWER – 192 State the domain and range of the function –y = ( 2 x – )2)2 3. + 4. ANSWER domain: all real numbers; range: y 3 ≤ 1. 5 2 – 3. – 3 4 2 1 +

9. Example 3 Graph an Exponential Function Graph the function. Describe the horizontal asymptote. State the domain and range. 2 x + 3 y = a. 2x2x y = b. – 3 The graph passes through and () 3, 1 – ( ).). 1, 4 – The graph’s asymptote is the x -axis. SOLUTION a.Sketch the graph of, which passes through and Then translate the graph 3 units to the left. 2x2x y = () 0, 1 () 2, 4.

10. Example 3 Graph an Exponential Function The domain is all real numbers, and the range is The graph ’ s asymptote is the line y = – 3.3. 0.0. y > The graph passes through and () 0, 2 – ( ).). 2, 1 b.Again, sketch the graph of. Then translate the graph 3 units down. 2x2x y = The domain is all real numbers, and the range is y > – 3.3.

11. Checkpoint 5. Graph the function. Describe the horizontal asymptote. State the domain and range. Graph an Exponential Function 3x3x y = 2 + ANSWER domain: all real numbers, range: 2y > 2;2; y =

12. Checkpoint Graph the function. Describe the horizontal asymptote. State the domain and range. Graph an Exponential Function 6. 4x4x y = – 5 ANSWER domain: all real numbers, range: 5;5; y = – y > – 5

13. 3 x 4 Checkpoint Graph the function. Describe the horizontal asymptote. State the domain and range. Graph an Exponential Function 7. y = – ANSWER domain: all real numbers, range: 0y > 0;0; y =

14. Checkpoint Graph the function. Describe the horizontal asymptote. State the domain and range. Graph an Exponential Function 8. 2 x + 2 y = ANSWER domain: all real numbers, range: 0y > 0;0; y =

23. Example 4 Model Exponential Growth Stock Market The annual number of shares S (in billions) traded on the New York Stock Exchange (NYSE) from 1990 to 2004 can be approximated by the model S where x is the number of years since 1990. Graph the model. Then use the graph to estimate the number of shares traded in 1999. ()x)x 1.2 39 = SOLUTION Make a table of values or list of ordered pairs : () x, Sx, S ( ),), 0, 39 ( ),), 2, 56 ( ),), 4, 81 ( ),), 6, 116 ( ),), 8, 168 ( ),), 10, 241 ( ),), 12, 348 () 14, 501

24. Example 4 Model Exponential Growth Plot the points. Draw a smooth curve through the points. ANSWER Using the graph, you can estimate that about 200 billion shares were traded in 1999.

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26. Geometry Link