Chapter 3 Exponential, Logistic, and Logarithmic Functions

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. Example Finding an Exponential Function from its Table of Values

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

10. Exponential Growth and Decay

11. Sketch exponential graph and determine if they are growth or decay

12. Example Transforming Exponential Functions

13. Example Transforming Exponential Functions

14. Example Transforming Exponential Functions

15. 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?

16. The Natural Base e

17. Exponential Functions and the Base e

18. Exponential Functions and the Base e

19. Example Transforming Exponential Functions

20. Example Transforming Exponential Functions

21. Logistic Growth Functions

22. Example: Graph and Determine the horizontal asymptotes

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

24. Group Work: Graph and determine the horizontal asymptotes

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

26. 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)

27. 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?

28. 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?

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

30. 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?

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

32. Exponential and Logistic Modeling

33. 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

34. Quick Review

35. Quick Review Solutions

36. Exponential Population Model

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

38. Example Finding Growth and Decay Rates

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

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

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

42. Answer • t=12.77 hours

43. Example Modeling Bacteria Growth

44. 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.

45. answer • Just the setting up

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

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

48. Example Modeling a Rumor

49. Example Modeling a Rumor: Answer

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