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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. Exponentialand logarithmicfunctions Yr 11 maths methods

  2. Objectives for Term 2 • To define and understand exponential functions. • To sketch graphs of the various types of exponential functions. • To understand the rules for manipulating exponential and logarithmic expressions. • To solve exponential equations. • To evaluate logarithmic expressions. • To solve equations using logarithmic methods. • To sketch graphs of functions of the form y = logax and simple transformations of this. • To understand and use a range of exponential models. • To sketch graphs of exponential functions. • To apply exponential functions to solving problems.

  3. Introduction • Functions in which the independent variable is an index number are called indicial or exponential functions. For example: • f (x) = ax where a > 0 and a ≠ 1 • quantities which increase or decrease by a constant percentage in a particular time can be modelled by an exponential function. • Exponential functions can be seen in everyday life for example in science and medicine (decay of radioactive material, or growth of bacteria like those shown in the photo), and finance ( compound interest and reducing balance loans).

  4. Index laws

  5. Multiplication • When multiplying two numbers in index form with the same base, add the indices. • For example, 23 × 24 =(2 × 2 × 2) × (2 × 2 × 2 × 2) = 27 am × an = am+ n

  6. Division • When dividing two numbers in index form with the same base, subtract the indices. am ÷ an = am- n

  7. Raising to a power • To raise an indicial expression to a power, multiply the indices. (am)n = am × n = amn

  8. Raising to the power of zero • Any number raised to the power of zero is equal to one. a0 = 1, a ≠ 0

  9. Products and quotients

  10. Remember

  11. Questions

  12. Answers (a)

  13. Answers (b)

  14. Answers (c)

  15. Answers (d)

  16. Homework • Page 220 Questions 1 – 3

  17. More Questions

  18. Answer without using your Cauculators

  19. Answer with your calculators

  20. Questions

  21. Answer (a)

  22. Answer (b)

  23. Question

  24. Answer

  25. Homework • Page 220 – 221 - Questions 4 – 10

  26. negative and rational powers

  27. negative powers

  28. Examples

  29. Answer A

  30. Answer B

  31. Rational powers

  32. Examples

  33. Examples

  34. Indicial equations

  35. Indicial equations

  36. Examples

  37. Answer A

  38. Answer B

  39. Answer C

  40. Solve the following

  41. Answer

  42. Answer

  43. Graphs of exponential functions

  44. Graphs of exponential functions

  45. The effect of changing the “a” coeff

  46. The effect of changing the “a” coeff

  47. The effect of changing the “a” coeff

  48. Reflections of exponential functions

  49. Reflections of exponential functions

  50. Reflections of exponential functions