1. Exponenetial and Logarithmic Functions Chapter Four

2. §4.1 Exponential Function (Review) Exponential function: 指数函数 if b is a positive number other than 1 (b>0, b≠1), there is a unique function called the exponential function with base b that is defined by f(x)=b x for every real number x

6. §4.1 The natural Exponential Base Definition: The natural exponential function is Where n10100100010,000100,000 2.593742.704812.716922.7118152.71827

7. §4.1 Continuous Compounding of Interest If P is the initial investment (the principal) and r is the interest rate (expressed as a decimal), the balance B after the interest is added will be B=P+P r =P(1+r) dollars to be continued

10. §4.1 Continuous Compounding of Interest

11. §4.1 Present value

13. §4.1 Exponential Growth and Decay

14. §4.2 Logarithmic Function ( 对数函数 )

15. §4.2 Graphs of Logarithmic Function

16. §4.2 The Natural Logarithm

17. §4.2 Doubling Time

18. §4.2 Half Time

19. §4.3 Differentiation of Logarithmic and Exponential Function

21. to be continued

25. §4.3 Differentiation of Exponential Function Differentiate both sides of the equation

26. to be continued

28. §4.3 Exponential Growth and Decay

30. §4.3 Logarithmic Differentiation Taking the derivatives of some complicated functions can be simplified by using logarithms. This is called logarithmic differentiation. to be continued

36. §4.3 Logarithmic Differentiation The relative rate of change of a quantity Q(x) can be computed by finding the derivative of lnQ.

37. §4.4 Additional Exponential Models Curve Sketching: to be continued

38. 2 min --------++++++ ( x 0 to be continued

42. 0 max ++++++-------- x ++++++ Inf 1 Inf Sign of ++++++ x

44. §4.4 Optimal Holding time

45. to be continued

47. §4.4 Learning Curve Learning Curve

48. §4.4 Learning Curve