Скачать презентацию Chapter 8 Exponential and Logarithmic Functions Exponential graph Скачать презентацию Chapter 8 Exponential and Logarithmic Functions Exponential graph

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Chapter 8: Exponential and Logarithmic Functions Exponential: graph, growth v. decay, natural number e Chapter 8: Exponential and Logarithmic Functions Exponential: graph, growth v. decay, natural number e Logs: graph, properties Solving equations

Exponential Functions n Equation ¨ Horizontal , where Asymptote: y=k GROWTH: b > 1 Exponential Functions n Equation ¨ Horizontal , where Asymptote: y=k GROWTH: b > 1 DECAY: 0 < b < 1 e is approximately 2. 618 Asymptote: y=0

Exponential Equations n Exponential Growth: n Exponential Decay: n Compound Interest: Exponential Equations n Exponential Growth: n Exponential Decay: n Compound Interest:

Example MC Questions 1. Which of the following correctly describes the function y = Example MC Questions 1. Which of the following correctly describes the function y = 2(⅛)3 x + 5 I. The function represents exponential growth II. The function represents exponential decay III. The range is y > 5 A) I only C) I and III only E) I, II, and III B) II only D) II and III only

Example MC Questions 2. What is the simplified form of (½e-4 x)-3 ? A) Example MC Questions 2. What is the simplified form of (½e-4 x)-3 ? A) B) C) D) E)

Example MC Questions 3. Suppose you buy a new car for $25, 000. The Example MC Questions 3. 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)t C) V(t) = 25, 000(1. 1)t D) V(t) = 25, 000(0. 91)t E) V(t) = 25, 000(-9)t

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

Logarithms n n n A logarithm is the inverse of an exponential function Remember: Logarithms n n n 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

Properties of Logs Properties of Logs

Example MC Questions 5. Which of the following is the exponential form of the Example MC Questions 5. Which of the following is the exponential form of the statement log 4 16384 = 7 A) 163841/7 = 4 B) 163847 = 7 C) 163841/4 = 7 D) 47 = 16384 E) 74 = 16384

Example MC Questions 6. Which of the following is equivalent to log 100 x³y Example MC Questions 6. Which of the following is equivalent to log 100 x³y 8? A) log 100 + log x³ + log y 8 B) 10 + 3 log x + 8 log y C) log 100 + (⅓)log x³ + (⅛)log y 8 D) log 10 + log 3 x + log 8 y E) 2 + 3 log x + 8 log y

Example MC Questions 7. Which of the following is equivalent to log 3 2? Example MC Questions 7. Which of the following is equivalent to log 3 2? I. III. A) I only B) II only C) I and III only D) II and III only E) I, II, and III

Example MC Questions 8. Consider the function y = e(x-3). What is the inverse Example MC Questions 8. Consider the function y = e(x-3). What is the inverse of the function? A) B) C) D) E)

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

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

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

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

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