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Chapter 8: Exponential and Logarithmic Functions

Review. Chapter 8: Exponential and Logarithmic Functions. Exponential: graph, growth v. decay, natural number e Logs: graph, properties Solving equations. Exponential Functions. Equation , where Horizontal Asymptote: y=k.

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Chapter 8: Exponential and Logarithmic Functions

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  1. Review Chapter 8: Exponential and Logarithmic Functions Exponential: graph, growth v. decay, natural number eLogs: graph, propertiesSolving equations

  2. Exponential Functions • Equation , where • Horizontal Asymptote: y=k GROWTH: b > 1DECAY: 0 < b < 1e is approximately 2.618 Asymptote: y=0

  3. Exponential Equations • Exponential Growth: • Exponential Decay: • Compound Interest:

  4. Example MC Questions • Which of the following correctly describes the function y = 2(⅛)3x + 5 I. The function represents exponential growthII. The function represents exponential decayIII. The range is y > 5A) I only B) II only C) I and III only D) II and III onlyE) I, II, and III

  5. Example MC Questions • What is the simplified form of (½e-4x)-3 ? A) B)C) D)E)

  6. Example MC Questions • Suppose you buy a new car for $25,000. The value, V, of the car decreases 9% each year. If t is the number of years since you purchased the car, which of the following functions gives the value of the car after t years?A) 25,000 = P(0.91)t B) V(t) = 25,000(9)tC) V(t) = 25,000(1.1)t D) V(t) = 25,000(0.91)t E) V(t) = 25,000(-9)t

  7. Example MC Questions 4. What function is graphed?A)B)C)D)E)

  8. Logarithms • A logarithm is the inverse of an exponential function • Remember: A log is an exponent!!! • Graph of a log – Vertical Asymptote: x=h Asymptote: x=2

  9. Properties of Logs

  10. Example MC Questions • Which of the following is the exponential form of the statement log4 16384 = 7 A) 163841/7 = 4 B) 163847 = 7 C) 163841/4 = 7 D) 47 = 16384 E) 74 = 16384

  11. Example MC Questions • Which of the following is equivalent to log 100x³y8? A) log 100 + log x³ + log y8 B) 10 + 3log x + 8log y C) log 100 + (⅓)log x³ + (⅛)log y8 D) log 10 + log 3x + log 8y E) 2 + 3log x + 8log y

  12. Example MC Questions • Which of the following is equivalent to log3 2? I. II. III.A) I only B) II only C) I and III only D) II and III onlyE) I, II, and III

  13. Example MC Questions • Consider the function y = e(x-3). What is the inverse of the function?A) B)C) D)E)

  14. Example MC Questions • Jill made a mistake in one of the steps in the following problem. Given -13 + ln x2 = -9 Step 1 ln x2 = 4 Step 2 2 ln x = 4 Step 3 ln x = 2 Step 4 elnx = e2 Step 5 x = 2e Which step is incorrect? A) Step 1 B) Step 2 C) Step 3 D) Step 4 E) Step 5

  15. Example MC Questions 10. Solve: ex-2 + 3 = 32A) 2 + log (29-e) B) -2 + log (29-e)C) 2 + ln 29 D) -2 + ln 29E) No solution

  16. Example MC Questions 11. What is the solution of 93x = 27x+2 ?A) 0 B) 1 C) 2D) 3 E) 4

  17. Example MC Questions 12. What is the solution of log2 (5x - 6) = 6A) 2 B) 6 C) 9 D) 11E) 14

  18. STUDY STUDY STUDY • These “MC” are GOOD questions. Study them well. • Final -seniors, Friday June 5th -all others, June 10th/11th

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