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Chapter 10

Chapter 10. Exponential and Logarithmic Functions. Lesson 10.1: Exponential Functions. Learning Targets:. • I can graph exponential functions . • I can determine if an exponential function is growth or decay . • I can write an exponential function given two points .

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Chapter 10

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  1. Chapter 10 Exponential and Logarithmic Functions

  2. Lesson 10.1:Exponential Functions

  3. Learning Targets: • I can graph exponential functions. • I can determine if an exponential function is growth or decay. • I can write an exponential function given two points. • I can solve equations involving exponents.

  4. Graphing an exponential function: y = a∙bxstandard form of an exponential function a = y-intercept (0, a) b = base x = exponent

  5. Example 1: Graphing Exponential Functions Sketch the graph of y = 4xand identify its domain and range. Domain:________ Range:_________

  6. Example 2: Graphing Exponential Functions Sketch the graph of y = 0.7xand identify its domain and range. Domain:________ Range:_________

  7. What type of function is it? Growth Decay

  8. Example 3:Indicate whether each exponential function is growth or decay. Decay Decay Growth

  9. Example 4:Write an exponential function whose graph passes through the given points. y = a∙bx (0, -2) and (3, -54)

  10. Example 5:Write an exponential function whose graph passes through the given points. y = a∙bx (0, 7) and (1, 1.4)

  11. Example 6:Write an exponential function whose graph passes through the given points. y = a∙bx (0, 3) and (-1, 6)

  12. Example 7:Write an exponential function whose graph passes through the given points. y = a∙bx (0, -18) and (-2, -2)

  13. Remember the Exponent Rules:

  14. Example 8:Simplify expressions. b. a.

  15. Example 8:Simplify expressions. c. d.

  16. Example 9: Solve equations. Step 1: Make the bases the same. Step 2: Set the exponents equal. Step 3: Solve.

  17. Example 10:Solve equations.

  18. Example 11:Solve equations.

  19. Home Fun 10-1 Worksheet

  20. Lesson 10-2: Logarithmic Functions Objectives: I can…. • Convert from logarithmic to exponential form and vice versa. • Evaluate logarithmic expressions. • Solve logarithmic equations.

  21. Definition of Logarithm: Let b > 0 and b 1. Then n is the logarithm of m to the base b, written logb m = n bn = m if and only if

  22. Check it out! Exponential FormLogarithmic Form means means means means means means means

  23. Example 1: Convert to exponential form. a. b.

  24. Example 1 (continued) c. d.

  25. Flower Power Root Rule Power Flower Power Root Root Root

  26. Example 2: Convert to logarithmic form. a. b.

  27. Example 2 (continued) c. d.

  28. Example 3: Evaluate logarithmic expressions. a.

  29. Example 3 (continued) b.

  30. A couple of intricate ones… c. d.

  31. Think-Pair-Share! b. a.

  32. Example 4: Solve logarithmic equations. a.

  33. Example 4 (continued) b.

  34. Example 4 (still continued!) c.

  35. Example 4 (last one!) d.

  36. Home Fun 10-2 Worksheet

  37. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  38. Transparency 3a

  39. Lesson 10-3: Properties of Logs Learning Targets: • I can use the product and quotient properties of logs. • I can use the power property of logs. • I can solve equations using properties of logs.

  40. Properties Product Property: Example: Quotient Property: Example: Power Property: Example:

  41. Example 1: Solving Equations

  42. Example 2: Solving Equations

  43. Your Turn : Solve each equation. a. b.

  44. Home 10-3 Worksheet

  45. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  46. Transparency 3a

  47. Algebra 2A – Lesson 10-4 Common Logarithms

  48. Lesson 10-4: Common Logs Learning Targets: • I can find common logarithms. • I can solve logarithmic and exponential equations. • I can use the Change of Base Formula.

  49. What is a Common Logarithm? This logarithm is used so frequently, that it is programmed into our calculators. We write it as: log m Note that we don’t write the base for a common log.

  50. Example 1: Find Common Logs with a Calculator Use a calculator to evaluate each logarithm to four decimal places. No base labeled, so it must be log10 (the common log). a) log 6 b) log 0.35

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