1 / 16

8-3: The Number ‘e’ (Day 1)

This lesson focuses on the laws of fractional exponents and the understanding of exponential functions involving growth and decay. Students will explore the natural base 'e', defined as approximately 2.718, through various examples and exercises. Key tasks include simplifying and evaluating natural base expressions, graphing exponential functions, and determining their characteristics such as domain and range. Students will apply their knowledge to complete exercises and demonstrate their understanding of exponential growth and decay phenomena.

pilis
Télécharger la présentation

8-3: The Number ‘e’ (Day 1)

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. 8-3: The Number ‘e’(Day 1) Objective (Ca. Standard 12): Students know the laws of fractional exponents, understand exponential function, and use these functions in problems in problems involving exponential growth and decay.

  2. Investigating the Natural Base e Turn to page 480 complete the table and answer the question in part 2.

  3. Do the values in the table appear to be approaching a fixed decimal number? Yes, the number 2.718.

  4. The Natural Base e The natural base e is irrational. It is defined as follows:

  5. Example 1: Simplifying Natural Base Expressions Simplify

  6. Example 2: Evaluating Natural Base Expressions

  7. Natural base exponential function has the form The function is an exponential growth function if a > 0 and r > 0.

  8. (2, 7.29) (1, 2.7) (0, 1)

  9. The function is an exponential decay function if a > 0 and r < 0. (-2, 7.29) (-1, 2.7) (0, 1)

  10. Example 3: Graphing Natural Base Functions Graph the function. State the domain and range. Solution: Because a = 2 is positive and r = 0.75, the function is an exponential growth function.

  11. Plot the points and sketch the graph. Domain: all real #’s Range: y > 0

  12. Solution: Because a= 1 is positive and r = - 0.5 is negative, the function is an exponential decay function.

  13. Translate the graph to the right by 2 units and up 1.

  14. Domain = all real #’s Range = y > 1

  15. Homework: P.483 #17-31 Odd, #49-59 Odd

More Related