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# Chapter 3 Exponential, Logistic, and Logarithmic Functions

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1. Chapter 3 Exponential, Logistic, and Logarithmic Functions

2. Quick Review

3. Quick Review Solutions

4. Exponential Functions

5. Determine if they are exponential functions

6. Answers • Yes • No • Yes • Yes • no

7. Sketch an exponential function

8. Exponential Growth and Decay

9. Example Transforming Exponential Functions

10. Example Transforming Exponential Functions

11. Example Transforming Exponential Functions

12. Group Activity • Use this formula • Group 1 calculate when x=1 • Group 2 calculate when x=2 • Group 3 calculate when x=4 • Group 4 calculate when x=12 • Group 5 calculate when x=365 • Group 6 calculate when x=8760 • Group 7 calculate when x=525600 • Group 8 calculate when x=31536000 • What do you guys notice?

13. The Natural Base e

14. Exponential Functions and the Base e

15. Exponential Functions and the Base e

16. Example Transforming Exponential Functions

17. Example Transforming Exponential Functions

18. Logistic Growth Functions

19. Example: Graph and Determine the horizontal asymptotes

20. Answer • Horizontal asymptotes at y=0 and y=7 • Y-intercept at (0,7/4)

21. Group Work: Graph and determine the horizontal asymptotes

22. Answer • Horizontal asymptotes y=0 and y=26 • Y-intercept at (0,26/3)

23. Word Problems: • Year 2000 782,248 people • Year 2010 923,135 people • Use this information to determine when the population will surpass 1 million people? (hint use exponential function)

24. Group Work • Year 1990 156,530 people • Year 2000 531,365 people • Use this information and determine when the population will surpass 1.5 million people?

25. Word Problem • The population of New York State can be modeled by • A) What’s the population in 1850? • B) What’s the population in 2010? • C) What’s the maximum sustainable population?

26. Answer • A) 1,794,558 • B) 19,161,673 • C) 19,875,000

27. Group Work In chemistry, you are given half-life formulas If you are given a certain chemical have a half-life of 56.3 minutes. If you are given 80 g first, when will it become 16 g?

28. Homework Practice • P 286 #1-54 eoe

29. Exponential and Logistic Modeling

30. Review • We learned that how to write exponential functions when given just data. • Now what if you are given other type of data? That would mean some manipulation

31. Quick Review

32. Quick Review Solutions

33. Exponential Population Model

34. Example: • You are given • Is this a growth or decay? What is the rate?

35. Example Finding Growth and Decay Rates

36. Example • You are given • Is this a growth or decay? What is the rate?

37. Example Finding an Exponential Function Determine the exponential function with initial value=10, increasing at a rate of 5% per year.

38. Group Work • Suppose 50 bacteria is put into a petri dish and it doubles every hour. When will the bacteria be 350,000?

40. Example Modeling Bacteria Growth

41. Group Work: half-life • Suppose the half-life of a certain radioactive substance is 20 days and there are 10g initially. Find the time when there will be 1 g of the substance.

42. answer • Just the setting up

43. Group Work • You are given • When will this become 150000?

44. Example Modeling U.S. Population Using Exponential Regression Use the 1900-2000 data and exponential regression to predict the U.S. population for 2003.

45. Example Modeling a Rumor

46. Example Modeling a Rumor: Answer

47. Key Word • Maximum sustainable population • What does this mean? What function deals with this?