Exponential and Logarithmic Functions

1. ExponentialandLogarithmic Functions By: Hendrik Pical to Revition Exponential and Logarithmic Functions Last Updated: January 30, 2011

2. With your Graphing Calculatorgraph each of the following y = 2x y = 3x y = 5x y = 1x Determine what is happening when the base is changing in each of these graphs.

3. y = 3x y = 2x

4. y = 3x y = 5x y = 2x y = 1x

5. y = 3x y = 5x y = 2x y = 4x y = 10x y = (3/2)x Determine where each of the following would lie? y=10x y=4x y = (3/2)x y = 1x

6. Exponential graphs with translations

7. f(x) = 2x

8. f(x) = 2x-3 x - 3 = 0 x = 3 (3, 1) 3

9. f(x) = 2x+2 - 3 x + 2 = 0 x = -2 3 2 (-2, -2) y = -3

10. flip flip f(x) = -(2)x-4 – 2 x - 4 = 0 x = 4 4 2 y = -2 (4, -3)

11. Compound Interest You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly? A = Final amount = unknown P = Principal = $5000 r = rate of interest = .045 n = number of times compounded per year = 4 t = number of years compounded = 10

12. Compound Interest You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly? A = unknown P = $5000 r = .045 n = 4 t = 10

13. Compound Interest You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly? weekly? A = unknown P = $5000 r = .045 52 n = 4 t = 10

14. Exponential DECAY

15. With your Graphing Calculatorgraph each of the following y = (1/2)x y = (1/3)x y = 1x Determine what is happening when the base is changing in each of these graphs.

16. y = (1/3)x y = 5x y = 2x y = 3x y = (½)x y = 1x Jeff Bivin -- LZHS

17. f(x) = 2-x = (1/2)x (0, 1) Jeff Bivin -- LZHS

18. f(x) = (½)x-3 - 2 = (2)-x+3 - 2 x - 3 = 0 x = 3 3 2 (3, -1) y = -2

20. A new Number We could use a spreadsheet to determine an approximation.

21. A new Number

22. y = 3x y = 2x Graph y = ex y = ex

23. Graph: y = ex+2 y = ex+2 y = ex x + 2 = 0 x = -2

24. Compound Interest-continuously You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded continuously? A = Final amount = unknown P = Principal = $5000 r = rate of interest = .045 t = number of years compounded = 10

25. Compound Interest-continuously You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded continuously? A = unknown P = $5000 r = .045 t = 10

26. Bacteria Growth You have 150 bacteria in a dish. It the constant of growth is 1.567 when t is measured in hours. How many bacteria will you have in 7 hours? y = Final amount = unknown n = initial amount = 150 k = constant of growth = 1.567 t = time = 7

27. Bacteria Growth You have 150 bacteria in a dish. It the constant of growth is 1.567 when t is measured in hours. How many bacteria will you have in 7 hours? y = unknown n = 150 k = 1.567 t = 7

29. y = 2x x = 2y INVERSE

30. y = 2x x = 2y INVERSE How do we solve this exponential equation for the variable y? ?

31. LOGARITHMS exponential logarithmic b > 0 A > 0

32. exponential logarithmic

33. Evaluate

34. Evaluate

35. Evaluate

36. Evaluate

37. Evaluate

38. Evaluate

39. y = 2x x = 2y INVERSE y=log2x

40. x = 2y y = log2x y = log3x y = log5x

41. x = (½)y y = log½x

42. Solve for x log2(x+5) = 4 24= x + 5 16= x + 5 11= x

43. Solve for x logx(32) = 5 x5= 32 x5 = 25 x = 2

44. Evaluate log3(25) = u 3u= 25 3u = 52 ??????

46. Change of Base Formula if b = 10

47. Evaluate log3(25) = 2.930

48. Evaluate log5(568) = 3.941

49. Properties of Logarithms • Product Property • Quotient Property • Power Property • Property of Equality

50. Product Property multiplication addition multiplication addition