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Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

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Exponential and Logarithmic Functions

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  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