Chapter 8: Exponential and Logarithmic Functions

Exponential: graph, growth v. decay, natural number eLogs: graph, propertiesSolving equations

Exponential Functions

Equation , where Horizontal Asymptote: y=k

Asymptote: y=0

GROWTH: b > 1DECAY: 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 growthII. The function represents exponential decayIII. The range is y > 5

A) I only B) II onlyC) I and III only D) II and III onlyE) I, II, and III

Example MC Questions

2. What is the simplified form of (½e-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

10log log

log lne

x x

x x

Example MC Questions

5. 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

Example MC Questions

6. 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

Example MC Questions

7. 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 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 x2 = -9Step 1 ln x2 = 4Step 2 2 ln x = 4Step 3 ln x = 2Step 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

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 93x = 27x+2 ?

A) 0 B) 1 C) 2

D) 3 E) 4

Example MC Questions

12. What is the solution of log2 (5x - 6) = 6

A) 2 B) 6

C) 9 D) 11

E) 14

STUDY STUDY STUDY

These “MC” are GOOD questions. Study them well.

Final

-seniors, Friday June 5th

-all others, June 10th/11th