Free Printable CIA #2 Review

1.

For each sequence, state if it is arithmetic, geometric, or neither.

-6, 24, 54, 84, 114...

a)

Arithmetic

b)

Geometric

c)

Neither

2.

For each sequence, state if it is arithmetic, geometric, or neither.

3, -6, 12, -24, 48,....

a)

Arithmetic

b)

Geometric

c)

Neither

3.

Which of the following choices is the formula for the nth term of the sequence?

-9375, -1875, -375, -75,...

a)

$a_n=-9375\left(-\frac{1}{5}\right)^{n-1}$

b)

$a_n=-9375\left(5\right)^{n-1}$

c)

$a_n=-9375\left(\frac{1}{5}\right)^{n-1}$

d)

$a_n=-9375\left(-5\right)^{n-1}$

4.

Write the recursive formula for the sequence.

21, 27, 33, 39, 45

a)

$a_n=a_{n-1}+6,\ a_1=21$

b)

$a_n=a_{n-1}+21,\ a_1=6$

c)

$a_n=a_{n-1}\cdot6,\ a_1=21$

d)

$a_n=6n+15$

5.

Write the recursive formula for the sequence.

2, -4, 8, -16, 32

a)

$a_n=a_{n-1}+6,\ a_1=2$

b)

$a_n=a_{n-1}\cdot2,\ a_1=-2$

c)

$a_n=a_{n-1}\cdot-2,\ a_1=2$

d)

$a_n=2\left(-2\right)^{n-1}$

6.

Write the explicit formula for the sequence.

-29, 1, 31, 61, 91

a)

$a_n=30n-29$

b)

$a_n=30n-59$

c)

$a_n=a_{n-1}+30,a_1=-29$

d)

$a_n=a_{n-1}\cdot2,\ a_1=-29$

7.

Write the explicit formula for the sequences.

-4, 16, -64, 256, -1024

a)

$a_n=-4\left(4\right)^{n-1}$

b)

$a_n=-4\left(-4\right)^{n-1}$

c)

$a_n=16\left(4\right)^{n-1}$

d)

$a_n=-4\left(\frac{1}{4}\right)^{n-1}$

8.

Given the explicit formula for the sequence find the recursive formula.

a_n=3\cdot4^{n-1}

a)

$a_n=a_{n-1}\cdot4,\ a_1=4$

b)

$a_n=a_{n-1}\cdot2,\ a_1=3$

c)

$a_n=a_{n-1}\cdot3,\ a_1=4$

d)

$a_n=a_{n-1}\cdot4,\ a_1=3$

9.

Given the explicit formula for the sequence find the recursive formula.

a_n=18+9n

a)

$a_n=a_{n-1}+9,\ a_1=34$

b)

$a_n=a_{n-1}+18,\ a_1=36$

c)

$a_n=a_{n-1}+18,\ a_1=9$

d)

$a_n=a_{n-1}+9,\ a_1=27$

10.

State if the sequence is arithmetic, geometric, or neither.

a_n=40\cdot\left(-\frac{1}{2}\right)^{n-1}

a)

Arithmetic

b)

Geometric

c)

Neither

11.

State if the sequence is arithmetic, geometric, or neither.

a_n=2\cdot5^{n-1}

a)

Arithmetic

b)

Geometric

c)

Neither

12.

State if the sequence is arithmetic, geometric, or neither.

a_n=\left(2n-1\right)^2

a)

Arithmetic

b)

Geometric

c)

Neither

13.

State if the sequence is arithmetic, geometric, or neither.

a_n=-46+10n

a)

Arithmetic

b)

Geometric

c)

Neither

14.

Given the first two terms of a sequence: 5, 20, ... write the explicit rule to represent the nth term if it is an arithmetic sequence.

a)

$a_n=5\left(4\right)^{n-1}$

b)

$a_n=5\left(15\right)^{n-1}$

c)

$a_n=15n-10$

d)

$a_n=5+15n$

15.

Given the first two terms of a sequence: 5, 20, ... write the explicit rule to represent the nth term if it is an geometric sequence.

a)

$a_n=5\left(4\right)^{n-1}$

b)

$a_n=5\left(15\right)^{n-1}$

c)

$a_n=15n-10$

d)

$a_n=5+15n$

16.

Find the explicit and recursive formula.

-15, -6, 3, 12,...

a)

b)

c)

d)

17.

Find the explicit formula and recursive formula.

4, -8, 16, -32,...

a)

b)

c)

d)

18.

Given the first two terms of an arithmetic sequence. Find the indicated term.

32, 24

Find a₃₈

a)

$-227$

b)

$-264$

c)

$-152$

d)

$-226$

19.

Given the explicit formula for a sequence find the term named in the problem.

a_n=-4\cdot2^{n-1},\ Find\ a_{12}

a)

$-\frac{1}{512}$

b)

$-10,240$

c)

$-\frac{5}{2048}$

d)

$-8,192$

20.

Given the explicit formula for a sequence find the term named in the problem.

a_n=16-3n,\ Find\ a_{40}

a)

-107

b)

-104

c)

-108

d)

-147

21.

Given the recursive formula for an arithmetic sequence find the 52nd term. $a_n=a_{n-1}-20,\ a_1=-30$

a)

-1152

b)

-1174

c)

-1050

d)

-1196

22.

Given the first two terms of a geometric sequence, find the indicated term.

3, -9, ...

Find a₁₂

a)

-531441

b)

6144

c)

531441

d)

2048

23.

$a_n=a_{n-1}\cdot2,\ a_1=-3$

Given the recursive formula for a geometric sequence find the explicit formula.

a)

$a_n=2\left(-3\right)^{n-1}$

b)

$a_n=-3\left(-2\right)^{n-1}$

c)

$a_n=-3\left(2\right)^{n-1}$

d)

$a_n=-6\left(-3\right)^{n-1}$

24.

Given the sequence below, what term of the sequence is 262?

-3, 2, 7,..., 262

a)

54

b)

7

c)

53

d)

57

25.

Lloya vacations in New York city. She dropped a marble off the top of the empire state building. The distance the marble will fall is 18 feet in the first second, 52 feet the next second, 86 feet an so on in an arithmetic sequence. What is the total distance the object will fall in eight seconds.

a)

34 ft

b)

222 ft

c)

256 ft

d)

290 ft

26.

Write the recursive formula for the following sequence?

6, 4, 2, 0, . . .

a)

a_n = -2n + 8

b)

a₁= 6,

a_n = a_n - 4

c)

a₁ = 6,

a_n = a_n-1 + 2

d)

a₁ = 6,

a_n = a_n-1 - 2

27.

Identify the common difference.
3, 7, 11, 15, ...

a)

6

b)

5

c)

4

d)

2

28.

Given the recursive formula below, find the first five terms.

u₁ = 3

u_n = u_n-1 + 2

a)

3, 5, 7, 9, 11

b)

5, 7, 9, 11, 13

29.

Given the sequence 4, 11, 18, 25...... what is a₃ ?

a)

4

b)

11

c)

18

d)

25

30.

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

a)

a_n = a_n-1 + 16

a₁= 17

b)

a_n = a_n-1 - 17

a₁= 17

c)

a_n = a_n-1 - 15

a₁= 17

d)

a_n = a_n-1 - 16

a₁= 17

31.

Given the recursive formula below, identify the common difference.

u₁ = 3

u_n = u_n-1 + 2

a)

3

b)

2

c)

n-1

d)

u₁

32.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n= a_n-1+ 11

a₁= 6

b)

a_n= a_n-1- 4

a₁= 6

c)

a_n= a_n-1+ 9

a₁= 6

d)

a_n= a_n-1+ 6

a₁= 6

33.

Which of the following is a recursive rule?

a)

a_n= 12+(n - 1)3

b)

a_n= a_n-1- 7

a₁= 5

c)

a_n= 7n - 2

d)

a_n= 7n + 12

34.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

35.

Given the recursive formula below, find the first four terms.

a₁ = 3

a_n = a_n-1 - 6

a)

3, -3, -9, -15

b)

-3, -9, -15, -21

c)

3, 9, 15, 21

d)

-3, 3, 9, 15

36.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n= a_n-1+ 11

a₁= 6

b)

a_n= a_n-1- 4

a₁= 6

c)

a_n= a_n-1+ 9

a₁= 6

d)

a_n= a_n-1+ 6

a₁= 6

37.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 7

a₁= 5

b)

a_n= a_n-1- 7

a₁= 5

c)

a_n= 7n - 2

d)

a_n= 7n + 5

38.

Which is the explicit formula for the sequence?

a)

a_n= a_n-1+ 7

a₁= 5

b)

a_n= a_n-1- 7

a₁= 5

c)

a_n= 7n - 2

d)

a_n= 7n + 5

39.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 3

a₁= 5

b)

a_n= a_n-1 + 5

a₁= 3

c)

a_n= 5n - 2

d)

a_n= 5n + 3

40.

Which is the explicit formula for the sequence?

a)

a_n= a_n-1+ 3

a₁= 5

b)

a_n= a_n-1 + 5

a₁= 3

c)

a_n= 5n - 2

d)

a_n= 5n + 3

41.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 14

a₁= 11

b)

a_n= a_n-1 + 11

a₁= 14

c)

a_n= 11n + 3

d)

a_n= 11n + 14

42.

Which is the explicit formula for the sequence?

a)

a_n= a_n-1+ 14

a₁= 11

b)

a_n= a_n-1 + 11

a₁= 14

c)

a_n= 11n + 3

d)

a_n= 11n + 14

43.

Select the recursive AND explicit formula for the sequence. (Pick BOTH)

a)

a_n= a_n-1- 12

a₁= 3

b)

a_n= a_n-1 + 12

a₁= 3

c)

a_n= -12n + 3

d)

a_n= -12n + 15

44.

Kate is trying to fatten up her prize pig for the FFA competition. The first week the pig weighs 163 lbs and each following week the pig is is gaining weight at a rate of 2 lbs per week. Write a recursive and explicit rule to represent pig’s weight at n weeks. (Pick BOTH)

a)

a_n= a_n-1+ 2

a₁= 163

b)

a_n= a_n-1+ 2

a₁= 161

c)

a_n= 2n + 161

d)

a_n= 2n + 165

45.

Jamie is trying to minimize the stress in his life and become more organized. The first month he makes a to-do list with 26 items on it. Every following month he is able to complete 7 items on his to-do list. Write a recursive rule to represent the remaining items on Janson’s to-do list at n months.

a)

a_n= a_n-1 - 7

a₁= 26

b)

a_n= a_n-1 + 7

a₁= 26

c)

a_n= a_n-1 + 26

a₁= 7

d)

a_n = -7n + 33

46.

Identify the common difference.
3, 7, 11, 15, ...

a)

6

b)

5

c)

4

d)

2

47.

Given the recursive formula below, identify the common difference.

a₁ = 3

a_n = a_n-1 + 2

a)

3

b)

2

c)

n-1

d)

$a_n$

48.

Identify the first term, given the recursive formula:

$a_n=a_{n-1}-3$

$a_1=-5$

a)

-3

b)

-5

c)

-4

d)

-8

49.

Given the first term and the common difference of an arithmetic sequence find the recursive formula.

$a_1=20\ and\ d=-3$

a)

$a_n=a_{n-1}+3$

$a_1=20$

b)

$a_n=a_{n-1}+20$

$a_1=-3$

c)

$a_n=a_{n-1}-3$

$a_1=20$

d)

$a_n=a_{n-1}-1$

$a_1=20$

50.

Write the recursive formula for the following sequence?

6, 4, 2, 0, . . .

a)

a_n = -2n + 8

b)

a₁= 6,

a_n = a_n - 6

c)

a₁ = 6,

a_n = a_n-1 + 2

d)

a₁ = 6,

a_n = a_n-1 - 2

51.

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

a)

a_n = a_n-1 + 16

a₁= 17

b)

a_n = a_n-1 - 17

a₁= 17

c)

a_n = a_n-1 - 15

a₁= 17

d)

a_n = a_n-1 - 16

a₁= 17

52.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n= a_n-1+ 11

a₁= 6

b)

a_n= a_n-1- 4

a₁= 6

c)

a_n= a_n-1+ 9

a₁= 6

d)

a_n= a_n-1+ 6

a₁= 6

53.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n= a_n-1+ 11

a₁= 6

b)

a_n= a_n-1- 4

a₁= 6

c)

a_n= a_n-1+ 9

a₁= 6

d)

a_n= a_n-1+ 6

a₁= 6

54.

Which of the following is a recursive rule?

a)

a_n= 12+(n - 1)3

b)

a_n= a_n-1- 7

a₁= 5

c)

a_n= 7n - 2

d)

a_n= 7n + 12

55.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 7

a₁= 5

b)

a_n= a_n-1- 7

a₁= 5

c)

a_n= 7n - 2

d)

a_n= 7n + 5

56.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 3

a₁= 5

b)

a_n= a_n-1 + 5

a₁= 3

c)

a_n= 5n - 2

d)

a_n= 5n + 3

57.

Which is the recursive formula for the sequence?

a)

a_n= a_n-1+ 14

a₁= 11

b)

a_n= a_n-1 + 11

a₁= 14

c)

a_n= 11n + 3

d)

a_n= 11n + 14

58.

Arithmetic sequences involve

a)

multiplication and division

b)

multiplication and addition

c)

addition and subtraction

d)

subtraction and division

59.

What kind of sequence?

400, 200, 100, 50, 25, ...

a)

Arithmetic

b)

Geometric

60.

What kind of sequence?

−34, −26, −18, −10, −2, ...

a)

Arithmetic

b)

Geometric

61.

What kind of sequence?

-4, -12, -36, -108,...

a)

arithmetic

b)

geometric

62.

What kind of sequence?

13, 9, 5, ...

a)

Arithmetic

b)

Geometric

63.

Geometric sequences involve

a)

multiplication

b)

multiplication and addition

c)

addition and subtraction

d)

subtraction and division

64.

What kind of sequence?

-8, -40, -200, ...

a)

Arithmetic

b)

Geometric

65.

What kind of sequence?

40, 43, 46, 49, 52, …

a)

arithmetic

b)

geometric

66.

What kind of sequence?

-4, 12, -36, 108, …

a)

arithmetic

b)

geometric

67.

What kind of sequence?

25, 125, 625, …

a)

arithmetic

b)

geometric

68.

What are the next 3 terms in this sequence of terms? 3, 7, 11, 15

a)

18, 22, 26

b)

19, 21, 23

c)

19, 23, 27

d)

18, 21, 24

69.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

70.

What is the common ratio for the sequence:
28, -14, 7, -3.5...

a)

1/2 (or 0.5)

b)

- 1/2 (or -0.5)

c)

-14

d)

-7

71.

Find the common ratio of the geometric sequence: -2, -4, -8, -16, . . .

a)

-2

b)

2

c)

4

d)

-4

72.

The difference between two terms in an arithmetic sequence is called ___________________.

a)

Formula

b)

Common Ratio

c)

Common Difference

d)

Common Factor

73.

In the sequence 9, 18, 27, 36 and so on, what is the common difference?

a)

5

b)

7

c)

9

d)

11

74.

Which kind of sequence has a common ratio?

a)

Arithmetic

b)

Geometric

75.

Determine if the sequence is arithmetic, geometric, or neither.

18, 25, 32, 39, 46

a)

Arithmetic

b)

Geometric

c)

Neither

76.

Determine if the sequence is arithmetic, geometric, or neither.

-1, -2, -4, -8, -16

a)

Arithmetic

b)

Geometric

c)

Neither

77.

Determine if the sequence is arithmetic, geometric, or neither.

a_n=2\left(-5\right)^{n-1}

a)

Arithmetic

b)

Geometric

c)

Neither

78.

Determine if the sequence is arithmetic, geometric, or neither.

a_n=15+10n

a)

Arithmetic

b)

Geometric

c)

Neither

79.

Write the explicit formula for the sequence.

4, 24, 144, 864, 5184

a)

$a_n=4\cdot6^{n-1}$

b)

$a_n=4\cdot3^{n-1}$

c)

$a_n=4\cdot12^{n-1}$

d)

$a_n=24\cdot\frac{1}{3}^{n-1}$

80.

Write the explicit rule for the sequence.

14, 20, 26, 32, 38,...

a)

$a_n=10+4n$

b)

$a_n=20-6n$

c)

$a_n=8+6n$

d)

$a_n=14+6n$

81.

Find the explicit formula.
-32, -16, -8, -4,...

a)

$a_n=-32\cdot5^{n-1}$

b)

$a_n=-32\left(\frac{1}{2}\right)^{n-1}$

c)

$a_n=-64\left(2\right)^{n-1}$

d)

$a_n=-32\left(\frac{1}{4}\right)^{n-1}$

82.

Write the recursive formula for the sequence.

4, 20, 100, 500, 2500,...

a)

$a_n=a_{n-1}\cdot4,\ a_1=4$

b)

$a_n=a_{n-1}\cdot2,\ a_1=4$

c)

$a_n=a_{n-1}\cdot\frac{1}{5},\ a_1=4$

d)

$a_n=a_{n-1}\cdot5,\ a_1=4$

83.

Given the explicit formula, find the 22nd term.

a_n=-33-5n

a)

-208

b)

-143

c)

-206

d)

-164

84.

Find the explicit formula and the recursive formula.

27, 19, 11, 3, ...

a)

b)

c)

d)

85.

Find the explicit formula and the recursive formula.

-4, 20, -100, 500,...

a)

b)

c)

d)

86.

The first two terms of an arithmetic sequence are 3 and 7 respectively. Which of the following represents the 21st term?

a)

79

b)

75

c)

87

d)

83

87.

The first two terms of a geometric sequence are 12 and 36 respectively. Which of the following represents the 9th term?

a)

78,732

b)

26,244

c)

2,592

d)

236,196

88.

Given the recursive formula for a geometric sequence find the term named in the problem.

a_n=a_{n-1}\cdot3,\ a_1=-3,\ Find\ \ \ \ a_9

a)

-6561

b)

-65536

c)

-19683

d)

19683

89.

Find the indicated term of the geometric sequence.

-2, -6, -18, -54,... Find a₉

a)

-13122

b)

-131072

c)

-4374

d)

13122

90.

Given the sequence below, what term of the sequence is 82?

2, 6, 10, 14, ... 82.

a)

21

b)

19

c)

32

d)

14

91.

Given the recursive formula for a geometric sequence find the explicit formula.

a_n=a_{n-1}\cdot6,\ a_1=-2

a)

$a_n=\frac{1}{2}\cdot4^{n-1}$

b)

$a_n=2\cdot-6^{n-1}$

c)

$a_n=-2\cdot6^{n-1}$

d)

$a_n=2\cdot4^{n-1}$

92.

A bacteria model shows the number of bacterial cells over time. The first hour there is 1 bacteria cell. The second hour there are 2 bacteria cells. The third hour there are 4 bacteria cells. The fourth hour there are 8 bacteria cells. How many bacteria cells will there be in 24 hours?

a)

4,194,304

b)

16,777,216

c)

6,223,980

d)

8,388,608

93.

Given the first two terms of a sequence: 4, 16, ...

Write the explicit rule to represent the nth term if it is an arithmetic sequence.

a)

$a_n=12n+16$

b)

$a_n=12n-8$

c)

$a_n=4n+16$

d)

$a_n=12n+4$

94.

Given the first two terms of a sequence: 4, 16, ...

Write the explicit rule to represent the nth term if it is an geometric sequence.

a)

$a_n=4\cdot8^{n-1}$

b)

$a_n=4\cdot12^{n-1}$

c)

$a_n=8\cdot2^{n-1}$

d)

$a_n=4\cdot4^{n-1}$

95.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

96.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

97.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

98.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

99.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

100.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

101.

Identify the asymptote.

a)

y = 0

b)

y = 2

c)

x = 0

d)

x = 2

102.

Identify the asymptote.

a)

y = -1

b)

y = 1

c)

x = -1

d)

y = 5

103.

Identify the asymptote.

a)

y = -1

b)

y = 5

c)

x = -1

d)

y = -3

104.

Identify the asymptote.

y=3\left(\frac{1}{2}\right)^x

a)

$y=0$

b)

$y=3$

c)

$y=2$

d)

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

105.

Identify the asymptote.

y=4\left(\frac{1}{5}\right)^x+3

a)

$y=0$

b)

$y=3$

c)

$y=4$

d)

$y=\frac{1}{5}$

106.

Identify the asymptote.

y=-3\left(2\right)^x-4

a)

$y=-3$

b)

$y=-4$

c)

$y=4$

d)

$y=2$

107.

Growth or Decay

y=-4\left(2\right)^x+3

a)

Growth

b)

Decay

108.

Growth or Decay

y=3\left(\frac{1}{2}\right)^x-1

a)

Growth

b)

Decay

109.

Which is the equation of the graph?

a)

$y=3\left(\frac{1}{2}\right)^x$

b)

$y=4\left(2\right)^x$

c)

$y=-3\left(2\right)^x+1$

d)

$y=-\frac{1}{2}\left(\frac{1}{2}\right)^x+1$

110.

Which is the equation of the graph?

a)

$y=3\left(\frac{1}{2}\right)^x$

b)

$y=4\left(2\right)^x$

c)

$y=3\left(2\right)^x+1$

d)

$y=-\frac{1}{2}\left(\frac{1}{2}\right)^x+1$

111.

Which is the correct graph of the following function:

y=-4\left(2\right)^x+2

a)

b)

c)

d)

112.

Which is the correct graph of the following function:

y=2\left(\frac{1}{2}\right)^x+2

a)

b)

c)

d)

113.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

114.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

115.

This is the horizontal line which the values of the function approach but not touch :

a)

Asymptote

b)

Growth Factor

c)

Axis of symmetry

d)

Curve

116.

True OR False: All increasing exponential functions eventually exceed all increasing linear functions.

a)

True

b)

False

117.

What functions describes this graph?

a)

Linear

b)

Exponential

c)

neither

118.

What is the general equation for a linear function?

a)

y=a\left(b\right)^x

b)

$y=ax^2+bx+c$

c)

$y=mx+b$

119.

What is the general equation for a exponential function?

a)

y=a\left(b\right)^x

b)

$y=ax^2+bx+c$

c)

$y=mx+b$

120.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

121.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

122.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

123.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

124.

You bought a Boston Whaler in 2004 for $12,500. The boat's value depreciates by 7% a year. How much is the boat worth in 2012?

a)

$11625

b)

$6994.77

c)

$21,477

d)

$875

125.

An exponential function has values shown below. If the exponential function was written, find the value of b.

a)

b = 0.25

b)

b = 4

c)

b = 16

d)

b = 0.5

126.

Which is the equation of the exponential function that passes through the points (0, 4) and (1, 8)?

a)

$y=2\left(4\right)^x$

b)

$y=4\left(2\right)^x$

c)

$y=4\left(1\right)^x$

d)

$y=8\left(2\right)^x$

127.

Is the ordered pair (2,6) a solution to the equation $y=4\left(1.5\right)^x$ ?

a)

NO

b)

YES

128.

Describe the transformation performed on the function.

$y=f\left(x\right)+8$

a)

Up 8

b)

Down 8

c)

Left 8

d)

Right 8

129.

Describe the transformation performed on the function.

$y=f\left(x+6\right)$

a)

Up 6

b)

Down 6

c)

Left 6

d)

Right 6

130.

Describe the transformation performed on the function.

$y=-f\left(x\right)$ .

a)

reflection in the x-axis

b)

horizontal translation left 1

c)

vertical stretch

d)

vertical translation down 1

131.

Describe the transformation performed on the function.

$y=5f\left(x\right)$

a)

vertical shrink by a factor of 5

b)

vertical stretch by a factor of 5

c)

horizontal shift left 5

d)

vertical shift down 5

132.

Identify the range of the function.

a)

$\left(-\infty,\infty\right)$

b)

$\left(1,\infty\right)$

c)

N/A

d)

$\left(-\infty,1\right)$

133.

Identify when the function is negative.

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,-2\right)$

c)

$\left(-\infty,-1\right)$

d)

$\left(2,\infty\right)$

134.

Identify the domain of the function.

a)

$\left(-2,\infty\right)$

b)

$\left(-\infty,2\right)$

c)

$\left(-\infty,\infty\right)$

d)

$\left(-1,\infty\right)$

135.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

136.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

137.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

138.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

139.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

140.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

141.

Determine whether the following is a growth or decay?

a)

Growth

b)

Decay

142.

Identify the asymptote.

a)

y = 0

b)

y = 2

c)

x = 0

d)

x = 2

143.

Identify the asymptote.

a)

y = -1

b)

y = 1

c)

x = -1

d)

y = 5

144.

Identify the asymptote.

a)

y = -1

b)

y = 5

c)

x = -1

d)

y = -3

145.

Identify the asymptote.

y=3\left(\frac{1}{2}\right)^x

a)

$y=0$

b)

$y=3$

c)

$y=2$

d)

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

146.

Identify the asymptote.

y=4\left(\frac{1}{5}\right)^x+3

a)

$y=0$

b)

$y=3$

c)

$y=4$

d)

$y=\frac{1}{5}$

147.

Identify the asymptote.

y=-3\left(2\right)^x-4

a)

$y=-3$

b)

$y=-4$

c)

$y=4$

d)

$y=2$

148.

Growth or Decay

y=-4\left(2\right)^x+3

a)

Growth

b)

Decay

149.

Growth or Decay

y=3\left(\frac{1}{2}\right)^x-1

a)

Growth

b)

Decay

150.

Which is the equation of the graph?

a)

$y=3\left(\frac{1}{2}\right)^x$

b)

$y=4\left(2\right)^x$

c)

$y=-3\left(2\right)^x+1$

d)

$y=-\frac{1}{2}\left(\frac{1}{2}\right)^x+1$

151.

Which is the equation of the graph?

a)

$y=3\left(\frac{1}{2}\right)^x$

b)

$y=-\frac{1}{2}\left(\frac{1}{2}\right)^x+1$

c)

$y=3\left(3\right)^x-1$

152.

Which is the correct graph of the following function:

$y=-4\left(2\right)^x+2$

a)

b)

c)

153.

Which is the correct graph of the following function:

y=2\left(\frac{1}{2}\right)^x+2

a)

b)

c)

d)

154.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

155.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

156.

This is the horizontal line which the values of the function approach but not touch :

a)

Asymptote

b)

Growth Factor

c)

Axis of symmetry

d)

Curve

157.

True OR False: All increasing exponential functions eventually exceed all increasing linear functions.

a)

True

b)

False

158.

What functions describes this graph?

a)

Linear

b)

Exponential

c)

neither

159.

What is the general equation for a linear function?

a)

y=a\left(b\right)^x

b)

$y=ax^2+bx+c$

c)

$y=mx+b$

160.

What is the general equation for a exponential function?

a)

y=a\left(b\right)^x

b)

$y=ax^2+bx+c$

c)

$y=mx+b$

161.

What is the End behavior on the right side

a)

x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$

162.

What is the End behavior on the left side

a)

$x\rightarrow-\infty,\ f\left(x\right)\rightarrow0$

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

163.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-3$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-3$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-3$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

164.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow3$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow3$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow3$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

165.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow2$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow2$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow8$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow2$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

166.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow0$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow0$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow8$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow0$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow0$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

167.

a)

A

b)

B

c)

C

d)

D

168.

a)

A

b)

B

c)

C

d)

D

169.

a)

$\infty$

b)

$-\infty$

c)

-3

d)

5

170.

a)

$\infty$

b)

$-\infty$

c)

3

d)

5

171.

a)

$\infty$

b)

$-\infty$

c)

3

d)

5

172.

a)

$\infty$

b)

$-\infty$

c)

0

d)

4

173.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow2$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow2$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow2$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow0$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow2$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

174.

Describe the end behavior

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-1$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow1$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow1$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-1$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

175.

Identify the formula.

y=a\left(1+r\right)^t

a)

Exponential Growth

b)

Compound Interest

176.

Identify the formula.

y=a\left(1+\frac{r}{n}\right)^{n\cdot t}

a)

Exponential Growth

b)

Compound Interest

177.

The population of a school is 800 students and is increasing at a rate of 2% per year. What will the population be in 6 years? Which would be the correct formula?

a)

$y=800\left(1+0.02\right)^6$

b)

$y=800\left(0.02\right)^6$

c)

$y=6\left(1+800\right)^2$

d)

$y=800\left(1+2\right)^6$

178.

The value of a violin was $32,000 when it was purchased new in 2005. The value appreciates at a rate of 15% per year. What is the value of the violin after in 2009?

a)

$55,968.20

b)

$16.20

c)

$112,572.04

d)

$65,800.55

179.

A condo in Austin, Texas, was worth $80,000 in 2000. The value of the condo increased by an average of 3% each year. Write an exponential function to model this situation. Then find the value of the condominium in 2005.

a)

$80,000.00

b)

$297,034.40

c)

$92,741.93

d)

$9,274.19

180.

Annual sales for a clothing store are $270,000 and are increasing at a rate of 7% per year; 3 years

a)

$1,326,510

b)

$92.61

c)

$330,761.61

d)

$420,225.61

181.

Given the equation for the population of a town 18,000(1.03)^x, what is the initial population?

a)

18,000

b)

1.03

c)

0.03

d)

x

182.

In 2010, the population of a town was 1000 and was growing at a rate of 5% per year. Write an exponential growth function to model this situation.

a)

$y=1000\left(1+0.05\right)^t$

b)

$y=1000\left(1+0.5\right)^t$

c)

$y=1000\left(0.05\right)^t$

d)

$y=1000\left(1+5\right)^t$

183.

Which of the following is the formula for Exponential Decay?

a)

$A=P\left(0.5\right)^t$

b)

$y=a\left(1-r\right)^t$

184.

The bird population in a forest is about 2300 and decreasing at a rate of 4% per year. Find the population in 10 years.

a)

1529

b)

2.4

c)

2135

d)

1450

185.

An internet chat room has 1200 participants and is declining at a rate of 2% per year. Find the number of participants in 5 years.

a)

1084

b)

1325

c)

1156

d)

1065

186.

In 1990, the population of a small Midwestern town is 4500. The population is decreasing at a rate of 1.5% per year. Write an exponential decay function to model this situation. Then find the number of people in the town in 2015.

a)

77

b)

308

c)

3084

d)

6529

187.

An investment of $8200 depreciates at rate of 2% per year. Which function models the value in 8 years?

a)

$y=8200\left(1.02\right)^8$

b)

$y=8200\left(0.98\right)^8$

c)

$y=8200\left(1.8\right)^8$

d)

$y=8200\left(0.8\right)^8$

188.

Which of the following is exponential decay?

a)

$y=7\left(1.06\right)^x$

b)

$y=500\left(0.89\right)^x$

c)

$y=6\left(1+0.15\right)^x$

d)

$y=400\left(1.001\right)^x$

189.

Which of the following is NOT exponential decay?

a)

$y=7\left(1.06\right)^x$

b)

$y=500\left(0.89\right)^x$

c)

$y=6\left(0.99\right)^x$

d)

$y=400\left(1-0.05\right)^x$

190.

Which of the following terms cannot be descirbed as exponential decay?

a)

depecriate

b)

decline

c)

half-life

d)

appreciate

e)

decrease

191.

Several years ago, Sean paid $18,000 for a new car. The function models the value V of the car, in thousands of dollars, t, years after he purchased it. If the car has been depreciating in value by 5% per year, when what is the value of b in the function?

$V\left(t\right)=18\left(b\right)^t$

a)

5

b)

1.05

c)

0.95

d)

1.8

CIA #2 Review

Total questions: 191

Worksheet time: 8hrs 33mins

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