Chapter 8 Exponential and Logarithmic Functions

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Chapter 8 Exponential and Logarithmic Functions by Mind Map: Chapter 8 Exponential and Logarithmic Functions

1. Chapter 8.1

2. Chapter 8.2

3. Chapter 8.3

4. Chapter 8.4

5. Chapter 8.5

6. Chapter 8.6

7. Exploring Exponential Models

8. Exponential function: is a funtion with the general form of y = ab^x

9. Growth factor: when b>1

10. Decay factor: when b <1

11. Asymtote: is a line that a graph approches as "x" or "y" increases in absolute value.

12. Properties of Exponential Functions

13. A = Pert A: amount in account P: Principle r: annual rate of intrest t: time in years

14. Logarithmis Functons as Inverses

15. Logarith: the base of a positive number.

16. Common logarith: is a logarithm that uses the base ten.

17. Logarithmis function: is a inverse of a exponential function.

18. Ex. log y = x b

19. Properties of Logarithms

20. Product Property: log(b) MN = log(b)M + log(b)N

21. Quotient Property: log(b) M/N = log(b)M - log(b)N

22. Power Property: log(b) M^x = x log(b)M

23. Exponential and Logarithmis Equations

24. Exponential equation: an equation in the form, b^cx = a.

25. Change of base formula: to evaluate a logarithm with any base.

26. Logarithmis equation: a equation that contains a logarithmic expression.

27. Ex. 7^3x = 20

28. 7^3x = 20 log7^3x = 20 3xlog7 = log20 x= log20/ 3log7 x=0.5132

29. Chapter 8.5

30. Natural Logarithms

31. Natural logarithm function: the functions inverse.

32. Ex. Write 3 ln 6 - ln 8 as a single natural logarithm

33. 3 ln 6 - ln 8 = ln 6^3 - ln 8 Power Property = ln 6^3/8 Quotient Property = ln 27 Simplify