exam 4

Question 1

12.1

A function that can be written in the form f(x) = b^x where b (1 BLANK) and b (2 BLANK), is called an exponential function with base b.

Two rules for the base of exponential functions.

Answer 1

1. Cannot be equal to 1.
2. Greater than 0. (b > 0)

Question 2

12.1

If f(x) = 3^x, find the following:
A. f(3)
B. f(0)
C. f(-2)

Answer 2

A. 27 (3^3)
B. 1 (3^0)
C. 1/9 (3^-2)

Question 3

12.1

If f(x) = 5 X 3^(x - 4) + 16, find f(6).

Plug it into x. Use a calculator.

Answer 3

61.

Question 4

12.1

An (BLANK) is a horizontal line that the graph of a function approaches as it moves to the right or left.

Answer 4

Asymptote.

Question 5

12.1

An (1 BLANK) increasing function is of the form f(x) = b^x where b is greater than (2 BLANK).

Answer 5

1. Expontentially
2. One

Question 6

12.1

When graphed, if the base is less than one, the graph is (BLANK).

Think of the oppposite direction.

Answer 6

Decreasing.

Question 7

12.1

The (BLANK) is denoated with the letter e.

Answer 7

natural base

Question 8

12.1

What is the natural exponential function?

Base “e”.

Answer 8

f(x) = e^x

Question 9

12.1

What button accounts for the natural expontential function (the natural base e)?

Answer 9

The “ln” button.

Question 10

12.1

If f(x) = e^x, find the following rounded to nearest thousandth:
A. f(5)
B. f(-1.7)
B. f(0)

Answer 10

A. 148.413
B. 0.183
C. 1

Question 11

12.1

For any positive real number b (b isn’t equal to 1) and any real numbers “r” and “s”, if b^r = b^s, then (BLANK).

One-to-one property of exponential functions.

Answer 11

r = s.

Question 12

12.1

Using one-to-one, solve the following:
A. 2^x = 16
B. 4^x = 256
C. 5^x = 1/125

Answer 12

A. x = 4
B. x = 4
C. x = -3

Question 13

12.1

Using one-to-one, solve the following:
3^(x + 2) = 1/27

Answer 13

x = -5

Question 14

12.2

For any positive real number b (b not equal to 1) and any positive real number “x”, we define LOGbx as the (BLANK) that “b” must be raised by to equal “x”.

LOGbx pronounced “the logarithm base b of x” or “log base b of x”

Definition of logarithm.

Answer 14

exponent

Question 15

12.2

Solve the following logarithmic function:

LOG3of9

What do you raise 3 by to get 9?

9 is the argument.

Answer 15

2.

This is the exponent of the base “3”.

Question 16

12.2

Solve the following logarithmic function:
LOG5of125

What do you raise 5 by to get 125?

125 is the argument.

Answer 16

3.

This is the exponent of the base “5”.

Question 17

12.2

For any positive real number “b” (b not equal to 1) and a positive real number “x”, we define f(x) = LOGbx as a logarithmic function.

The function f(x) is defined only for values of “x” greater than 0, so the (BLANK) is (0, infinity).

Think of the two axis on a graph.

Answer 17

domain

Question 18

12.2

Given the function f(x) = log2ofx, find f(16).

Plug in 16 to x.

Answer 18

4.

Question 19

12.2

We define the common logarithm whose base is (BLANK).

We write LOGx rather than LOG10ofx.

Common logarithm.

Answer 19

10.

Question 20

12.2

Evaluate the given logarithm. Round to nearest thousandth.
A. log100
B. log0.001
C. log75

Common logarithm.

Answer 20

A. 2
B. -2
C. 1.875

Remember base of 10.

Question 21

12.2

The natural logarithm, denoted with lnx is a logarithm whose base is (BLANK).

Answer 21

e

Remember “lnx = LOGeofx”.

Question 22

12.2

Evaluate the given logarithms. Round to the nearest thousandth.
A. lne^7
B. ln65
C. ln27.3

Answer 22

A. 7
B. 4.174
C. 3.307

Question 23

12.2

What are the two conversion formulas between exponential form and logarithmic form?

Answer 23

Expontential form:
B^x = Y
Logarithmic form:
LOGBofY = X

“Y” is the argument, “B” is the base, “X” is the exponent

Question 24

12.2

Rewrite the following in logarithmic form:
A. 2^-8 = 1/156
B. 7^x = 25
C. 3^x = 350

Answer 24

A. LOG2of(1/156) = -8
B. LOG7of(25) = x
C. LOG3of(350) = x

Question 25

# 12.2 Rewrite the following in exponential form: A. LOG3ofX = 6 B. lnx = 7 C. log100 = x

Answer 25

A. 3^6 = x B. e^7 = x C. 10^x = 100

Question 26

# 12.3 Define the product rule for logarithms.

Answer 26

LOG[base]B[of]X + LOG[base]B[of]Y = LOG[base]B[of]XY

Question 27

# 12.3 Define the power rule for logarithms.

Answer 27

LOG[base]b[of]X^r = R * LOG[base]b[of]X

Question 28

# 12.3 LOG[base]B[of]B^r = ?

Answer 28

r

Question 29

# 12.3 Define the change of base formula below. LOG[base]B[of]X = ?

Answer 29

LOG[base]A[of]X / LOG[base]A[of]B OR ln[of]X / ln[of]B | TIP: Remember you divide the argument of the LOG on top and the base of

Question 30

# 12.4 When solving exponential and logarithimic equations, what should you try to do first?

Answer 30

Get the same base (if possible).

Question 31

# 12.4 The one-to-one property of logarithimic functions basically says that as long as the LOGS have the same base then...

Answer 31

The arguments are equal. OR The exponents when written in exponential form.

Question 32

# 12.5 What is the compound interest formula?

Answer 32

A = P (1 + r/n)^nt

Question 33

# 12.5 What does each component represent in the compound interest formula? A = P (1 + r/n)^nt

Answer 33

P = principle amount R = interest rate (as decimal) T = time (in years) N = number of compounds (per year)

Question 34

# 12.5 What is the continuous interest formula?

Answer 34

A = Pe^rt

Question 35

# 12.5 What does each component represent in the continuous compound interest formula? A = Pe^rt

Answer 35

A = amount (after t years) P = principle R = interest rate (as a decimal) T = time (in years)

Question 36

# 12.5 What is the exponential growth/decay formula? | Hint: only formula with "p naught."

Answer 36

P = P(0)e^kt

Question 37

# 12.5 What does each component represent in the exponential growth/decay formula? P = P(0)e^kt

Answer 37

P = size (at time of t) P(0) = initial size K = constant T = time

Question 38

# 12.6 When graphing an exponential function, what part of the equation represents the asymptote value? | Hint: think of the standard form of an exponential equation.

Answer 38

The "K" value. It will always affect the y-axis.

Question 39

# 12.6 When graphing a logarithmic function, what part of the equation represents the aymptote value?

Answer 39

The "H" value. It will always affect the x-axis.

Question 40

# 12.6 What is the standard form of an exponential equation?

Answer 40

f(x) = B^(x-h) - 4

Question 41

# 12.6 What is the standard form of a logarithmic equation?

Answer 41

f(x) = LOG[base]B(x-h) + k

Question 42

# 12.6 When graphing logarithmic and exponential functions, what can you do first to help find the shift in your graph? | HINT: the first table of points you want to make.

Answer 42

Make (at least) 3 points of the parent graph.

Question 43

# 12.6 What do the "H" and the "K" in the standard forms affect in the graph?

Answer 43

The "h" value affects the x-axis and the "k" value affects the y-axis.