1 / 83

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: January 30, 2008. With your Graphing Calculator graph each of the following. y = 2 x. y = 3 x. y = 5 x. y = 1 x.

starr
Télécharger la présentation

Exponential and Logarithmic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ExponentialandLogarithmic Functions By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: January 30, 2008

  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. Jeff Bivin -- LZHS

  3. y = 3x y = 2x Jeff Bivin -- LZHS

  4. y = 3x y = 5x y = 2x y = 1x Jeff Bivin -- LZHS

  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 Jeff Bivin -- LZHS

  6. Exponential graphs with translations Jeff Bivin -- LZHS

  7. f(x) = 2x Jeff Bivin -- LZHS

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

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

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

  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. Jeff Bivin -- LZHS

  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 Jeff Bivin -- LZHS

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

  20. A new Number

  21. y = 3x y = 2x Graph y = ex y = ex Jeff Bivin -- LZHS

  22. Graph: y = ex+2 y = ex+2 y = ex x + 2 = 0 x = -2 Jeff Bivin -- LZHS

  23. 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

  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 = unknown P = $5000 r = .045 t = 10

  25. 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

  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 = unknown n = 150 k = 1.567 t = 7

  27. y = 2x x = 2y INVERSE Jeff Bivin -- LZHS

  28. y = 2x x = 2y INVERSE How do we solve this exponential equation for the variable y? ? Jeff Bivin -- LZHS

  29. LOGARITHMS exponential logarithmic b > 0 A > 0 Jeff Bivin -- LZHS

  30. exponential logarithmic Jeff Bivin -- LZHS

  31. Evaluate Jeff Bivin -- LZHS

  32. Evaluate Jeff Bivin -- LZHS

  33. Evaluate Jeff Bivin -- LZHS

  34. Evaluate Jeff Bivin -- LZHS

  35. Evaluate Jeff Bivin -- LZHS

  36. Evaluate Jeff Bivin -- LZHS

  37. y = 2x x = 2y INVERSE y=log2x Jeff Bivin -- LZHS

  38. x = 2y y = log2x y = log3x y = log5x Jeff Bivin -- LZHS

  39. x = (½)y y = log½x Jeff Bivin -- LZHS

  40. Solve for x log2(x+5) = 4 24= x + 5 16= x + 5 11= x Jeff Bivin -- LZHS

  41. Solve for x logx(32) = 5 x5= 32 x5 = 25 x = 2 Jeff Bivin -- LZHS

  42. Evaluate log3(25) = u 3u= 25 3u = 52 ?????? Jeff Bivin -- LZHS

  43. Change of Base Formula if b = 10 Jeff Bivin -- LZHS

  44. Evaluate log3(25) = 2.930 Jeff Bivin -- LZHS

  45. Evaluate log5(568) = 3.941 Jeff Bivin -- LZHS

  46. Properties of Logarithms • Product Property • Quotient Property • Power Property • Property of Equality Jeff Bivin -- LZHS

  47. Product Property multiplication addition multiplication addition Jeff Bivin -- LZHS

More Related