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 Asymptote: y=0 GROWTH: b > 1 DECAY: 0 < b < 1 e is approximately 2.618

Exponential Equations Exponential Growth: Exponential Decay: Compound Interest:

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

Example MC Questions 2. What is the simplified form of ( ½ e -4x ) -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 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 = 7 A) /7 = 4 B) = 7 C) /4 = 7D) 4 7 = E) 7 4 = 16384

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

Example MC Questions 7. Which of the following is equivalent to log 3 2? I. II. III. A) I onlyB) II only C) I and III onlyD) 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-13 + ln x 2 = -9 Step 1ln x 2 = 4 Step 2 2 ln x = 4 Step 3ln x = 2 Step 4 e lnx = e 2 Step 5x = 2e Which step is incorrect? A) Step 1B) Step 2C) Step 3 D) Step 4E) Step 5

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

Example MC Questions 11. What is the solution of 9 3x = 27 x+2 ? A) 0B) 1C) 2 D) 3E) 4

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

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