This document is a lecture on exponential and logarithmic functions that includes definitions and properties of exponential functions with various bases as well as examples and exercises. It introduces exponential functions where b>1 and 0<b<1 and their characteristics. It also covers the base-e exponential function, converting between bases, and applications of exponential functions through examples such as population growth, radioactive decay, and compound interest. The document concludes with a series of exercises related to exponential functions and their applications.

1. EXPONENTIAL AND LOGARTHMIC FUNCTIONS A Lecture By Abdul Ghaffar Khan

2. EXPONENTIAL FUNCTIONS g (x)= (0.5) x

3. Properties

4. Example 1

5. Example 1

6. Class of exp. function

7. Example 2

8. Example 3

9. CHARACTERSTICS OF f (x)=b x b > 1

10. Example 4

11. CHARACTERSTICS OF f (x)=b x , 0 < b < 1

12. Base-e Exponential function

13. Example 5

14. Conversion of base

15. Exercise 7.1

16. Exercise 7.1

17. Exercise 7.1

18. Exercise 7.1

19. 7.2 Applications

20. Example 6

21. Example 6

22. Example 7

23. Example 7

24. Example 8

25. Example 8

26. Example 9

27. Example 9

28. Example 10

29. Example 10

30. Example 11

31. Example 11

32. Exercise 7.2

33. Exercise 7.2

34. Exercise 7.2

35. Exercise 7.2

36. Exercise 7.2