Quiz about Sequences and Exponential Functions

Question 1

Find the 22nd term of the following sequence:
5, 8, 11, ...

Accepted Answer

68

Answer

14

Answer

63

Answer

71

Question 2

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

Accepted Answer

4

Answer

6

Answer

5

Answer

2

Question 3

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

Accepted Answer

a_n= -4n + 29

Answer

a_n = 4n + 29

Answer

a_n = -4n + 25

Answer

a_n = 4n + 25

Question 4

The next two terms of the sequence 12,17,22,27 are

Accepted Answer

27 and 32

Answer

28 and 33

Answer

29 and 34

Answer

30 and 35

Question 5

What is the common ratio for the sequence:
3, 15, 75...

Accepted Answer

5

Answer

12

Answer

1/5

Question 6

What is the explicit rule for the sequence:
11, 22, 44, 88...

Accepted Answer

a_n = 11(2)^n-1

Answer

a_n = 2(11)^n-1

Answer

an = 11x2

Question 7

Which formula is used to find the explicit equation for arithmetic sequences?

Accepted Answer

a_n = a₁ + d(n-1)

Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ * r^n-1

Question 8

Which formula is used to find the recursive equation for arithmetic sequences?

Accepted Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 9

Which formula is used to find the explicit equation for geometric sequences?

Accepted Answer

a_n = a₁ * r^n-1

Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ + d(n-1)

Question 10

Which formula is used to find the recursive equation for geometric sequences?

Accepted Answer

a_n = a_n-1 * r

Answer

a_n = a_n-1 + d

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 11

Is the graph linear, exponential or neither?

Accepted Answer

Linear

Answer

Exponential

Answer

Neither

Question 12

Which is the Next/Now rule for the table?

Accepted Answer

Next = Now x 9

Answer

Next = Now + 16

Answer

Next = Now x 6

Question 13

Is this exponential growth or decay?

Accepted Answer

Decay

Answer

Growth

Question 14

What type of function is y = 7(5/4)^x?

Accepted Answer

Exponential Growth

Answer

Exponential Decay

Answer

Linear

Answer

None of the above

Question 15

If f(x) = 2x-9, what is f(3)?

Accepted Answer

-3

Answer

6

Answer

3

Answer

-6

Question 16

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

y=5000(0.7)^x

Answer

y=30(5000)^x

Answer

y=5000(1.3)^x

Answer

y=5000xx

Question 17

What type of function best models the situation: A zombie virus has infected the population and the number of infected people triples every day.

Accepted Answer

exponential growth

Answer

linear

Answer

quadratic

Answer

exponential decay

Question 18

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

Accepted Answer

INITIAL VALUE

Answer

SLOPE

Answer

RATE OF CHANGE

Answer

COMMON RATIO

Question 19

Which graph below represents exponential decay?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Question 20

Which equation below represents exponential decay?

Accepted Answer

y = 2(1/4)^x

Answer

y = 3x - 5

Answer

y = 3(5)x

Question 21

Fill in the blank: In tables of exponential functions, you ___________ by the same amount each time to get to the next number.

Accepted Answer

multiply

Answer

add

Answer

subtract

Question 22

Fill in the blank: Graphs of exponential functions are ____________________.

Accepted Answer

curves

Answer

parabolas

Answer

lines

Question 23

Which table below models exponential growth?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Question 24

In order for an exponential function to show decay, the base must be ____________.

Accepted Answer

a fraction between 0 and 1

Answer

negative

Answer

a whole number

Question 25

Graph y = 3(5)^x

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Question 26

In the equation for an exponential function, where is the variable x?

Accepted Answer

in the exponent

Answer

in the base

Answer

it can be both in the base and the exponent

Question 27

Question 27.

Accepted Answer

C.

Answer

A.

Answer

B.

Answer

D.

Question 28

Which function is linear?

Accepted Answer

h(x)

Answer

f(x)

Answer

g(x)

Question 29

Which function is exponential?

Accepted Answer

g(x)

Answer

f(x)

Answer

h(x)

Question 30

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.

Accepted Answer

y=6(1.14)^x

Answer

y=6(0.14)^x

Answer

y=6(1+14)^x

Answer

y=6(0.86)^x

Question 31

The expression 5(2)^tgives the number of leaves in a plant as a function of the number of weeks since it was planted. What does 2 represent in this expression?

Accepted Answer

The number of leaves is multiplied by 2 each week.

Answer

There were initially 2 leaves in the plant.

Answer

The plant was planted 2 weeks ago.

Question 32

The expression 3(1.5)^t models the number of bacteria in a culture as a function of the number of hours since the culture was created. What does 3 represent in this expression?

Accepted Answer

There were initially 3 bacteria in the culture.

Answer

The number of bacteria is multiplied by 3 each hour.

Answer

The culture was created 3 hours ago

Question 33

Is the sequence geometric or arithmetic?
3, 6, 9, 12...

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Neither

Question 34

Is the sequence geometric or arithmetic?
6, 18, 54...

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Question 35

What is the 15th term of the sequence an = -3n+50

Accepted Answer

5

Answer

95

Answer

-5

Answer

-95

Question 36

Determine the first 3 terms of the following sequence.

t₁= -3

t_n=t_n-1(3)

Accepted Answer

-3, -9, -27

Answer

-3, 9, 27

Answer

-3, -6, -9

Answer

-3, 6,9

Question 37

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

Accepted Answer

17

Answer

14

Answer

13

Answer

16

Question 38

Create the explicit formula for the sequence:

2, 8, 14, ...

Accepted Answer

an=6n-4

Answer

an=2+6n

Answer

an=-6+6n

Answer

an=4-6n

Question 39

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

Accepted Answer

a₁= 10

a_n= a_n-1 - 5

Answer

a₁= 10

a_n= a_n-1 + 5

Answer

a₁= 10

a_n= a_n (5)

Answer

a₁= 10

a_n= a_n-1 (5)

Question 40

Write a recursive formula for the following sequence:

16,8, 4, 2,...

Accepted Answer

a₁=16

a_n=a_n-1 (1/2)

Answer

a₁=16

a_n=a_n-1 (2)

Answer

a₁=16

a_n=a_n-1 + (1/2)

Answer

a₁=16

a_n=a_{n-1 +} (2)

Question 41

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

Accepted Answer

True

Answer

False

Sequences and Exponential Functions

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