Free Printable Ch 6. Quiz 1. Review

1.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

2.

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Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

3.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

4.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

5.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

6.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

7.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

8.

Use the change of base rule to rewrite this problem:

log₇729

a)

log(7)/log(729)

b)

log(729)/log(7)

9.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

10.

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Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

11.

Without a calculator, determine which of the following yields a negative answer.

a)

log₉(¹/₃₀)

b)

log₉3

c)

log₉-81

d)

log₉1

12.

Without a calculator, evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

13.

Without a calculator, evaluate log₆ -36

a)

not possible

b)

-2

c)

2

d)

¹/2

14.

The equation $A=1750\left(1.04\right)^t$ represents an account balance t years after the account was created. Which is correct?

a)

The account balance will decrease 0.04% each year

b)

The account balance will increase 0.04% each year

c)

The account balance will decrease 4% each year

d)

The account balance will increase 4% each year

15.

The expression $89,000\left(0.995\right)^t$ represents the population of a town t years after 1990.

a)

The population is increasing.

b)

The population is decreasing.

16.

The population of deer on an island is given by $P\left(x\right)=100\left(0.85\right)^x$ , where x represents the number of years. What is the percent rate of change for the population of deer?

a)

85% decrease

b)

15% decrease

c)

85% increase

d)

15% increase

17.

A business manager has a starting annual salary of $42,000. Each year, the business manager will get a salary increase of 5.5%. Which function represents the business manager's salary, S, after t years?

a)

$S=42,000\left(1.55\right)^t$

b)

$S=42,000\left(1.055\right)^t$

c)

$S=42,000+1.55t$

d)

$S=42,000+0.055t$

18.

Which functions represent exponential decay? Select ALL that apply.

a)

$f\left(x\right)=\left(0.2\right)^x$

b)

$f\left(x\right)=0.2\left(2\right)^x$

c)

$f\left(x\right)=\left(2\right)^x$

d)

$f\left(x\right)=2\left(0.2\right)^x$

e)

$f\left(x\right)=2\left(2\right)^x$

19.

A new website has 25,000 visitors each week when it first launches. The number of visitors increases by 3% each week. Which function, V(t), represents the number of visitors t weeks after the website first launches?

a)

$V\left(t\right)=25,000+0.03t$

b)

$V\left(t\right)=25,000+1.03t$

c)

$V\left(t\right)=25,000\left(0.03\right)^t$

d)

$V\left(t\right)=25,000\left(1.03\right)^t$

20.

Which functions represent exponential growth? Select all that apply.

a)

$f\left(x\right)=5\left(\frac{1}{2}\right)^x$

b)

$f\left(x\right)=\frac{1}{2}\left(5\right)^x$

c)

$f\left(x\right)=\left(\frac{5}{2}\right)^x$

d)

$f\left(x\right)=\left(\frac{2}{5}\right)^x$

e)

$f\left(x\right)=2\left(\frac{1}{5}\right)^x$

21.

An experiment started with 100 bacteria at 10:00am. They double in number every hour. Find the number of bacteria at 2:00pm.
Find the missing value $B\left(?\right)\ =\ 100\left(2\right)^?$

a)

10

b)

2

c)

4

d)

100

22.

An experiment started with 100 bacteria. They double in number every hour. Find the number of bacteria after 8 hours.
Find the answer

a)

25,600 bacteria

b)

656,100 bacteria

c)

1,223,000 bacteria

d)

500,640,000 bacteria

23.

You deposit $1400 in an account that pays 6% interest compounded yearly. Find the balance for 20 years.
Find r (rate of increase)

a)

1400

b)

6% = 0.06

c)

1+0.06

d)

20

24.

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You deposit $1400 in an account that pays 6% interest compounded yearly. Find the balance for 20 years. Find the answer

a)

$2800.31

b)

$3564.22

c)

$4489.99

d)

$5298.26

25.

W(t) = 60(1-0.25)^t
Find a(initial amount)

a)

60

b)

25%

c)

1-0.25

d)

t

26.

P(6) = 3500 (1-.33)⁶
Find P(6) = ??
This means find the answer

a)

2345

b)

4.52

c)

316.6

d)

19,372.2

27.

Solve the radical equation: $11=2+\sqrt{90-x}$

a)

x = 9

b)

x = 82

c)

x = -9

d)

x = -82

28.

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Solve the radical equation: $6+\sqrt{6-15x}=15$

a)

x = -5

b)

x = 1/5

c)

No Solution

d)

x = -1

29.

Which operation is opposite to the operation of cubing a number?

a)

Addition

b)

Division

c)

Square

d)

Cube Root

30.

Which operation is opposite to the operation of taking the Square Root?

a)

Addition

b)

Division

c)

Square

d)

Cube Root

31.

Select the operation that is the opposite operation to Multiplication.

a)

Addition

b)

Division

c)

Squared

d)

Cube Root

32.

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Solve and check your solution(s)

$\sqrt[3]{x-9}=3$

a)

36

b)

18

c)

-18

d)

27

33.

Solve the equation:
^x/₃+ 10 = 15

a)

75

b)

15

c)

25

d)

5

34.

$2x^3+85=771$

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a)

$x=7$

b)

$x=-7$

c)

$x=\pm7$

d)

No Solution

35.

$5x^2=45$

a)

$x=\pm9$

b)

$x=3$

c)

$x=\pm3$

d)

$x=\pm15$

36.

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(x + 1) ² = 25

a)

± 5

b)

4 or -6

c)

-4 or 6

d)

± 4

37.

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Factor completely. k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

38.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

39.

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Factor 3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

40.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

41.

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x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

42.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

43.

Rewrite in exponential form:

log₉x=2

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

44.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

45.

Write 5^x =10 in log form

a)

x = log 5

b)

x = log₅10

c)

x = 5 log10

d)

x = 10 log 5

46.

Write in logarithmic form:

a^b = c

a)

log _a c = b

b)

log _b c = a

c)

log _a b = c

d)

log _b a = c

47.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

48.

Does the graph represent growth, decay, linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

49.

Given the equation below determine the y-intercept.

y=3^x

a)

(0, 1)

b)

(0, 3)

c)

x= 0

d)

y = 0

50.

Given the equation below determine the y-intercept.

y=3\left(3\right)^x

a)

(0, 1)

b)

(0, 3)

c)

x= 0

d)

y = 0

51.

What is the y-intercept of the function?

a)

none

b)

all real numbers

c)

(0, 80)

52.

What is the definition of an asymptote?

a)

a curved line

b)

a curve at the origin

c)

a line that continually approaches a given curve but does not meet it at any finite distance

53.

What is the horizontal asymptote?

a)

y =2

b)

y =-2

c)

x=-2

54.

Is the graph exponential growth or decay?

a)

Exponential growth

b)

Exponential decay

55.

Is the following function exponential growth, exponential decay, linear, or none of the above?
p(x) = 13x - 5

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

56.

What is the y-intercept?

a)

(0,0)

b)

(0,1)

c)

(-3,0)

d)

(0,-3)

57.

For exponential functions, the asymptotes are always...

a)

a horizontal line

b)

a vertical line

c)

a diagonal line

58.

Which of the following is an example of a graph of an exponential function?

a)

b)

c)

d)

59.

Which table represents the inverse function values of the table above?

a)

b)

c)

d)

60.

True or False? The inverse of (-5,6) is (6,-5)

a)

True

b)

False

61.

Which of the following tables represents the inverse function values of the table above?

a)

b)

c)

d)

62.

Which of the following tables represents the inverse function values of the table above?

a)

b)

c)

d)

63.

Which is the inverse of the table?

a)

b)

c)

d)

64.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

65.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

Ch 6. Quiz 1. Review

Total questions: 65

Worksheet time: 2hrs 20mins

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