Question
Question 1
A)Create a sequence to show exponential growth where the population of 120 is doubling every day.(1 point)
Responses

120, 360, 1,080 . . .
120, 360, 1,080 . . .

120, 60, 30 . . .
120, 60, 30 . . .

120, 240, 480, 360, 480 . . .
120, 240, 480, 360, 480 . . .

120, 240, 480 . . .
120, 240, 480 . . .
Question 2
A)Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . ..(1 point)
Responses

y=2(1.75)x−1
y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline

y=2(1.5)x
y equals 2 left parenthesis 1.5 right parenthesis superscript x baseline

y=2+1.75x
y equals 2 plus 1.75 x

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction
Question 3
A)
Use the image to answer the question.

Which of the following situations could describe the graph?
(1 point)
Responses

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

Juveldy puts $20 in a high-yield savings account. His investment triples every year.
Juveldy puts $20 in a high-yield savings account. His investment triples every year.

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

There are 200 cockroaches in a building, and the population triples every day.
There are 200 cockroaches in a building, and the population triples every day.
Question 4
A)Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?(1 point)
Responses

The graph will have a constant rate of change.
The graph will have a constant rate of change.

The points on the graph will have a common ratio of 32.
The points on the graph will have a common ratio of 32.

The points on the graph will have a common ratio of 1.32.
The points on the graph will have a common ratio of 1.32.

The graph will begin with the point (1,5) because Lori starts with five fish.
The graph will begin with the point left parenthesis 1 comma 5 right parenthesis because Lori starts with five fish.
Question 5
A)
Use the image to answer the question.

What is the initial value of the sequence?
(1 point)
Responses

0.5
0.5

0
0

1
1

2
2
page 16 of 16


A)Create a sequence to show exponential growth where the population of 120 is doubling every day.(1 point)
Responses

120, 360, 1,080 . . .
120, 360, 1,080 . . .

120, 60, 30 . . .
120, 60, 30 . . .

120, 240, 480, 360, 480 . . .
120, 240, 480, 360, 480 . . .

120, 240, 480 . . .
120, 240, 480 . . .
Question 2
A)Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . ..(1 point)
Responses

y=2(1.75)x−1
y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline

y=2(1.5)x
y equals 2 left parenthesis 1.5 right parenthesis superscript x baseline

y=2+1.75x
y equals 2 plus 1.75 x

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction
Question 3
A)
Use the image to answer the question.

Which of the following situations could describe the graph?
(1 point)
Responses

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

Juveldy puts $20 in a high-yield savings account. His investment triples every year.
Juveldy puts $20 in a high-yield savings account. His investment triples every year.

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

There are 200 cockroaches in a building, and the population triples every day.
There are 200 cockroaches in a building, and the population triples every day.
Question 4
A)Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?(1 point)
Responses

The graph will have a constant rate of change.
The graph will have a constant rate of change.

The points on the graph will have a common ratio of 32.
The points on the graph will have a common ratio of 32.

The points on the graph will have a common ratio of 1.32.
The points on the graph will have a common ratio of 1.32.

The graph will begin with the point (1,5) because Lori starts with five fish.
The graph will begin with the point left parenthesis 1 comma 5 right parenthesis because Lori starts with five fish.
Question 5
A)
Use the image to answer the question.

What is the initial value of the sequence?
(1 point)
Responses

0.5
0.5

0
0

1
1

2
2
page 16 of 16


Answers
GPT-4o mini
Let's go through each question one by one:
### Question 1
A) **Create a sequence to show exponential growth where the population of 120 is doubling every day.**
The correct response is:
**120, 240, 480 ...**
(This shows the population starting at 120 and doubling each day:
- Day 0: 120
- Day 1: 240
- Day 2: 480)
### Question 2
A) **Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125, 10.71875 ....**
The correct response is:
**y=2(1.75)^(x−1)**
(This formula represents the growth of the sequence, where the first term is 2 and it multiplies by 1.75 as x increases.)
### Question 3
A) **Which of the following situations could describe the graph?**
The appropriate response likely corresponds to an exponential growth scenario:
**Juveldy puts $20 in a high-yield savings account. His investment triples every year.**
(This describes exponential growth due to the tripling of the investment over time.)
### Question 4
A) **Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?**
The correct response is:
**The points on the graph will have a common ratio of 1.32.**
(This is because each month the number of fish increases by 32%, leading to a multiplicative factor of 1.32, consistent with exponential growth.)
### Question 5
A) **What is the initial value of the sequence?**
The answer depends on the specified sequence in the image (which I can't see), but if you presume the sequence starts at its first term provided:
If 0.5 is the first term of the sequence, the correct response is:
**0.5**
Otherwise, if the sequence starts at a different value (0, 1, or 2), choose the appropriate initial value based on that context.
If you have specific details or clarifications for any part of these questions, feel free to share for more tailored answers!
### Question 1
A) **Create a sequence to show exponential growth where the population of 120 is doubling every day.**
The correct response is:
**120, 240, 480 ...**
(This shows the population starting at 120 and doubling each day:
- Day 0: 120
- Day 1: 240
- Day 2: 480)
### Question 2
A) **Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125, 10.71875 ....**
The correct response is:
**y=2(1.75)^(x−1)**
(This formula represents the growth of the sequence, where the first term is 2 and it multiplies by 1.75 as x increases.)
### Question 3
A) **Which of the following situations could describe the graph?**
The appropriate response likely corresponds to an exponential growth scenario:
**Juveldy puts $20 in a high-yield savings account. His investment triples every year.**
(This describes exponential growth due to the tripling of the investment over time.)
### Question 4
A) **Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?**
The correct response is:
**The points on the graph will have a common ratio of 1.32.**
(This is because each month the number of fish increases by 32%, leading to a multiplicative factor of 1.32, consistent with exponential growth.)
### Question 5
A) **What is the initial value of the sequence?**
The answer depends on the specified sequence in the image (which I can't see), but if you presume the sequence starts at its first term provided:
If 0.5 is the first term of the sequence, the correct response is:
**0.5**
Otherwise, if the sequence starts at a different value (0, 1, or 2), choose the appropriate initial value based on that context.
If you have specific details or clarifications for any part of these questions, feel free to share for more tailored answers!