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Exponential and Logistic Functions: Modeling Growth Patterns

Learn about exponential functions, their graphs, the natural base e, logistic functions, and population models. Explore how these functions can model various growth patterns, such as the growth of human and animal populations.

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Exponential and Logistic Functions: Modeling Growth Patterns

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  1. 3.1 Demana, Waits, Foley, Kennedy Exponential and Logistic Functions

  2. What you’ll learn about • Exponential Functions and Their Graphs • The Natural Base e • Logistic Functions and Their Graphs • Population Models … and why Exponential and logistic functions model many growth patterns, including the growth of human and animal populations.

  3. Exponential Functions

  4. Example Finding an Exponential Function from its Table of Values

  5. Example Finding an Exponential Function from its Table of Values

  6. Exponential Growth and Decay What is this saying??

  7. Example: Transforming Exponential Functions

  8. Solution

  9. Solution

  10. Solution

  11. The Natural Base e If you had $1 and comounded it at 100% interest, how much would you have after one year if it were compounded; Monthly, weekly, daily, by the minute, by the second, or continuously???

  12. Exponential Functions and the Base e Interpret this

  13. Changing to base e

  14. Exponential Functions and the Base e Exponential Growth Exponential Decay

  15. Example: Transforming Exponential Functions

  16. Solution

  17. Solution

  18. Solution

  19. Logistic Growth Functions

  20. Homework • From textbook: 3.1 page 361, know 1 - 58

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