Chapter 8 Exponential and Logarithmic Functions Exponential graph

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 DECAY: 0 < b < 1 e is approximately 2. 618 Asymptote: y=0

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

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) B) C) D) E)

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)

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

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 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? 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 of the function? A) B) C) D) E)

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 (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 ? A) 0 B) 1 D) 3 E) 4 C) 2

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 June 5 th -all others, June 10 th/11 th