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math 044 college algebra > exam 4 > Flashcards

exam 4 Flashcards

1
Q

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.

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

12.1

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

A

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

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3
Q

12.1

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

Plug it into x. Use a calculator.

A

61.

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4
Q

12.1

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

A

Asymptote.

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5
Q

12.1

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

A
  1. Expontentially
  2. One
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6
Q

12.1

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

Think of the oppposite direction.

A

Decreasing.

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7
Q

12.1

The (BLANK) is denoated with the letter e.

A

natural base

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8
Q

12.1

What is the natural exponential function?

Base “e”.

A

f(x) = e^x

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9
Q

12.1

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

A

The “ln” button.

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10
Q

12.1

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

A

A. 148.413
B. 0.183
C. 1

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11
Q

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.

A

r = s.

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12
Q

12.1

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

A

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

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13
Q

12.1

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

A

x = -5

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14
Q

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.

A

exponent

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15
Q

12.2

Solve the following logarithmic function:

LOG3of9

What do you raise 3 by to get 9?

9 is the argument.

A

2.

This is the exponent of the base “3”.

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16
Q

12.2

Solve the following logarithmic function:
LOG5of125

What do you raise 5 by to get 125?

125 is the argument.

A

3.

This is the exponent of the base “5”.

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17
Q

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.

A

domain

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18
Q

12.2

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

Plug in 16 to x.

A

4.

19
Q

12.2

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

We write LOGx rather than LOG10ofx.

Common logarithm.

A

10.

20
Q

12.2

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

Common logarithm.

A

A. 2
B. -2
C. 1.875

Remember base of 10.

21
Q

12.2

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

A

e

Remember “lnx = LOGeofx”.

22
Q

12.2

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

A

A. 7
B. 4.174
C. 3.307

23
Q

12.2

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

A

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

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

24
Q

12.2

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

A

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

25
Q

12.2

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

A

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

26
Q

12.3

Define the product rule for logarithms.

A

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

27
Q

12.3

Define the power rule for logarithms.

A

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

28
Q

12.3

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

A

r

29
Q

12.3

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

A

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

30
Q

12.4

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

A

Get the same base (if possible).

31
Q

12.4

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

A

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

32
Q

12.5

What is the compound interest formula?

A

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

33
Q

12.5

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

A

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

34
Q

12.5

What is the continuous interest formula?

A

A = Pe^rt

35
Q

12.5

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

A

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

36
Q

12.5

What is the exponential growth/decay formula?

Hint: only formula with “p naught.”

A

P = P(0)e^kt

37
Q

12.5

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

A

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

38
Q

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.

A

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

39
Q

12.6

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

A

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

40
Q

12.6

What is the standard form of an exponential equation?

A

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

41
Q

12.6

What is the standard form of a logarithmic equation?

A

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

42
Q

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.

A

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

43
Q

12.6

What do the “H” and the “K” in the standard forms affect in the graph?

A

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

math 044 college algebra (4 decks)

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