Free Printable College m2

1.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

2.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

3.

This is an example of: $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

4.

How do you know that this was exponential decay? $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Because the 25 was bigger than one

b)

Because the 0.20 was bigger than one

c)

Because the 25 was less than one

d)

Because the 0.20 was less than one

5.

This is an example of: $f\left(x\right)=\ 0.25\ \left(\ 1.3\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

6.

How do you know that this was exponential growth? $f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$

a)

Because the 0.25 was bigger than one

b)

Because the 1.3 was bigger than one

c)

Because the 0.25 was less than one

d)

Because the 1.3 was less than one

7.

This is an example of: $f\left(x\right)=90\ \left(\ \frac{1}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

8.

How do you know that this was exponential decay? $f\left(x\right)=90\ \left(\ \frac{1}{2}\right)^x$

a)

Because the 90 was bigger than one

b)

Because the 1/2 was bigger than one

c)

Because the 90 was less than one

d)

Because the 1/2 was less than one

9.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ How many ants did you begin with?

a)

There was 2 ants

b)

There was 3 ants

c)

The equation doesn't tell us

10.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ What is the growth rate?

a)

The ants are growing by 3 times

b)

The ants are growing by 2 times

c)

The equation doesn't tell us

11.

If the decay rate is 20%, which of the following represent the decay factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

12.

If the growth rate is 80%, what is the growth factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

13.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

14.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

15.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

16.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

17.

Is this exponential growth or decay?

a)

Growth

b)

Decay

18.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

19.

Which of the followings functions shows an initial amout of $15 and an increase of 35% ?

a)

y=15(35)^x

b)

y=15(1.35)^x

c)

y=15(0.35)^x

d)

y=35(15)^x

20.

You invest $400 for 5 years and the interest rate is 4.29% each year.

a)

y=400(1 - 0.0429)⁵

b)

y=400(1+.0429)⁵

c)

y=400(1+ 4.29)⁵

d)

y=400e^0.049*5

21.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1 + .08)^x

c)

y=15,000(1 - .08)^x

d)

y=15,000(0.08)^x

22.

Identify the common ratio (multiplier) of the function f(x)=2(4)^x.

a)

2

b)

4

c)

(2)^x

d)

8

23.

What is the growth factor of the situation represented by f(x)=10(0.3)^x?

a)

10

b)

0.3

c)

1

d)

3

24.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

25.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

26.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

27.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

28.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

29.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

30.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

31.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

32.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

33.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

34.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

35.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

36.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

37.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

38.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

39.

Which of the following graphs is NOT an exponential function?

a)

b)

c)

d)

40.

Which function best describes the following graph?

a)

y = Log₂ X

b)

2^x = y

c)

y = 1/(2x)

d)

(1/2)^x = y

41.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

42.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

43.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

44.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

45.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

46.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

47.

ln(e^W)

a)

e

b)

W

c)

e^W

d)

undefined

48.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

49.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

50.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

51.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

52.

Find the corresponding graph of
$-\log_2\left(x\right)+3$

a)

b)

c)

d)

53.

Find the corresponding graph of
$\log_3\left(x-1\right)+4$

a)

b)

c)

d)

54.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

55.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

56.

Solve for x.
5^x = 1

a)

0

b)

-1

c)

2

d)

1

57.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

58.

Logarithmic functions have...

a)

Vertical asymptote at x=0

b)

Vertical asymptote at x=1

c)

Horizontal asymptote at y=1

d)

Horizontal asymptote at y=0

59.

$\log_6\left(x+4\right)=\ \log_6\left(2x-5\right)$

Solve the given equation:

a)

{-9)

b)

(9)

c)

(-1}

d)

()

60.

$e^{4x}=\ 5$

Solve the given equation:

a)

$x=\frac{\ln e}{4}$

b)

$x=\frac{4}{5}$

c)

$x=\frac{\ln\ \left(4\right)}{5}$

d)

$x=\frac{\ln\left(5\right)}{4}$

61.

$y=\log\left(3x-9\right)$

Find the domain of the function:

a)

$x\in\left(-\infty,3\right]$

b)

$x\in\left(-\infty,3\right)$

c)

$x\in\left[3,+\infty\right)$

d)

$x\in\left(3,+\infty\right)$

62.

$\log\left(x-1\right)+\log\left(x+1\right)=\log\left(3\right)$

Solve for x

a)

$x=\left\{-2,2\right\}$

b)

$x=\left\{2\right\}$

c)

$x\ =\left\{\sqrt{1001}\right\}$

d)

$x=\left\{\right\}$

63.

$2\log_5y\ -\ \frac{1}{2}\log_5x$

Write it as a single expression

a)

$\frac{\log_5y}{2\log5x}$

b)

$\log_5\left(\frac{y^2}{\sqrt{x}}\right)$

c)

$\log_5y^2+\log_5\sqrt{x}$

d)

$\log_5\left(\frac{y^2}{2x}\right)$

64.

What is the vertical asymptote for the graph of :

y = ln (7 - 14x)

a)

$x\ =\ 2$

b)

$x\ =-\ \frac{1}{2}$

c)

$x\ =\frac{1}{2}$

d)

$y\ =\ \frac{1}{2}$

65.

Write the logarithmic equation in the exponential form:

log (x-2) = -1

a)

$10^{-1}=\ x-2$

b)

$10\ ^x-2\ =-1$

c)

$\ln\ \left(x-2\right)\ =-1$

d)

$\left(x-2\right)^{-1}=10$

66.

$5^{\left(x+1\right)}=7$

Write the exponential equation as a logarithmic form

a)

$\log_5\left(x+1\right)=7$

b)

$\log_7\left(x+1\right)\ =5$

c)

$\log_5\left(7\right)=x\ +1$

d)

$\log_7\left(5\right)=\ x+1$

67.

$f\left(x\right)\ =\ e^{\left(2x-5\right)}-9\$

Write the domain of the function:

a)

$x\in\left(-\infty,+\infty\right)$

b)

$x\in\left(-\infty,\frac{5}{2}\right)$

c)

$x\in\left(\frac{5}{2},+\infty\right)$

d)

$x\in\left(-9,+\infty\right)$

68.

$m\left(x\right)\ =e^{\ 7x\ }-8$

Determine the horizontal asymptote of the function:

a)

$y\ =7x$

b)

$y\ =\ 8$

c)

$y=-\ 8$

d)

$y=\ 0$

69.

a)

A

b)

B

c)

C

d)

D

70.

Condense

a)

A

b)

B

c)

C

d)

D

71.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

72.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

73.

a)

A

b)

B

c)

C

d)

D

74.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

75.

Solve log₂ (2 - 2x) + log₂ (1 - x) = 5

a)

4

b)

5

c)

-2

d)

-3

76.

Solve log₅ (x + 3) = log₅ x + log₅ 3

a)

3/2

b)

9/2

c)

2/3

d)

No Solution

77.

Solve ln (x - 2) - ln (3x) = 0

a)

-1

b)

2

c)

e

d)

e⁵

78.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

79.

log₅ (2x - 3)² = 6

a)

x = 128

b)

x = 64

c)

x = 4

d)

x = 14

80.

Solve the equation for x.

a)

22.198

b)

e

c)

1.131

d)

21.66

81.

log x - log 8 = 3

a)

x = 1000

b)

x = 800

c)

x = 8000

d)

x = 100

82.

According to the logarithmic properties: $e^{\ln x}=x$

a)

True

b)

False

83.

Use the logarithmic properties to condense the expression correctly. $6\log x+2\log y$

a)

$\log x^6y^2$

b)

$\log_6x\log_2y$

c)

$\log\frac{x^6}{y^2}$

d)

$12\log xy$

84.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

85.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

86.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

87.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

88.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

College m2

Total questions: 88

Worksheet time: 7hrs 59mins

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