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Date: Lesson 8.1

Date: Lesson 8.1. I can graph exponential growth functions; graph exponential decay functions. Common Core: CC.9-12.F.IF.7e CRS: FUN 501. Topic : Exponential Growth.

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Date: Lesson 8.1

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  1. Date:Lesson 8.1

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

  3. 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

  4. Bell Ringer

  5. Warm-Up Exercises Warm-Up Exercises 2. • 5 23 ( – )2 x 2 3. • – 3 42 1 + y – = State the domain and range of the function 4. 3. + Evaluate the expression without using a calculator. 1. 5 2 –

  6. Warm-Up Exercises Warm-Up Exercises 1 ANSWER 25 y ≤ 3 ANSWER 40 2. • 5 23 ( – )2 x 2 3. • ANSWER – – 192 3 42 1 + y – = State the domain and range of the function 4. 3. + domain: all real numbers; range: ANSWER Evaluate the expression without using a calculator. 1. 5 2 –

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

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

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

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

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

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

  13. Example 4 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 1.2 39 = SOLUTION Make a table of values or list of ordered pairs : ( ) x,S ( ), ( ), ( ), ( ), 0, 39 2, 56 4, 81 6, 116 ( ), ( ( ( ) ), ), 8, 168 10, 241 12, 348 14, 501 Model Exponential Growth

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

  15. EXIT SLIP

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