1 / 19

Exponential Growth Functions

Exponential Growth Functions. AII, 12.0: Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. . Recap of last week. What did we learn last week? Exponential Properties Revisited (7) 296

ivy
Download Presentation

Exponential Growth Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Exponential Growth Functions AII, 12.0: Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

  2. Recap of last week • What did we learn last week? • Exponential Properties Revisited (7) 296 • Logarithm Properties (3) 442 • Special Logarithm properties (3 inverses)434 • Equality properties 448 • Change of Base Formula 440

  3. Overview for today Quiz (40 minutes MAX) Objectives • Logarithm expressions • Evaluate the expression • Properties of Logarithms • Expand expressions • Condense expressions • Solving Exponential and Logarithmic Equations • Equal powers property • Take the common logarithm • Extraneous solutions • Graph exponential growth functions

  4. General information you NEED Translating Exponential Functions • If |a|>1, the graph is vertically expanded • If 0<|a|<1, the graph is vertically compress • If a is negative, the graph is reflected about the x-axis • h represents an horizontal shift on the graph • k represents a vertical shift on the graph

  5. Objective: Exponential Growth Exponential Growth Graphs (pg412) • when a>0 and b>1 • The graph rises from left to right • The graph passes through (0,a) and (1,ab) • The domain is all real numbers • The range is y>0

  6. Example 1 1 1 SOLUTION 2 4 a 1 = y ab x = > b 1 x 0 1 2 3 2 1 y 1 2 4 8 – – Graph when and Graph the function y 2x. = Make a table of values for the function.

  7. Example 1 a 1 = y ab x = > b 1 Graph when and Plot the points from the table. Draw a curve that passes through the plotted points, as shown.

  8. Example 2 = • y 2 3x. = 2 2 1 3 9 4 SOLUTION a. Make a table of values. Then plot the points. > b 1 1 2 3 – – – x 0 1 2 y 2 6 27 Graph when and y ab x a 1 = a. Graph b. Graph • y 2x. = Draw a curve that passes through the plotted points, as shown at the right.

  9. Example 2 = 1 1 1 8 2 4 x 0 1 2 3 > b 1 y 1 2 1 – Graph when and y ab x a 1 = b. Make a table of values. Then plot the points. Draw a curve that passes through the plotted points, as shown at the right.

  10. Checkpoint y 5x = ANSWER y ab x = > b 1 2. ANSWER Graph when Graph the exponential function. 1. y 4x =

  11. Checkpoint • y 4 3x = ANSWER y ab x = > b 1 • y 0.1 2x = 4. ANSWER Graph when Graph the exponential function. 3.

  12. Properties of Exponential Functions State the Domain and Range Horizontal Asymptote • The Domain • Majority of the time all the real numbers • The range • Majority of the time from the horizontal asymptote and above • The horizontal asymptote is the minimum y-value. • Majority of the time it will be the k value from the general form:

  13. 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.

  14. 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

  15. 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 + =

  16. 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 =

  17. 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 = –

  18. 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.

  19. Conclusion Summary Assignment • What does the graph of an exponential growth function look like? • The graph of an exponential growth function of the form • Exponential Growth Pg415 #(17-39 ODD, 42-47EC) • Problems not finished will be left as homework.

More Related