Question
23.
A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5000 wasps, the situation can be modeled by which equation?
(1 point)
Responses
w(t) = 5000(13)t
where w(t) is the number of wasps after t months
w(t) = 5000(13)t
where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months
w(t) = 5000(87)t
where w(t) is the number of wasps after t months
w(t) = 5000(87)t
where w(t) is the number of wasps after t months
w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
Question 2
24.
Which of the following statements is true about the above wasp equation?
(1 point)
Responses
As t increases, w increases slowly at first and then quickly
As t increases, w increases slowly at first and then quickly
As t increases, w increases quickly at first and then slowly
As t increases, w increases quickly at first and then slowly
As t increases, w decreases slowly at first and then quickly
As t increases, w decreases slowly at first and then quickly
As t increases, w decreases quickly at first and then slowly
As t increases, w decreases quickly at first and then slowly
Question 3
25.
Given the explicit formula for the sequence in function notation, find the 5th term of the sequence.
f(n) = 2n−1
(1 point)
f(5) =
Question 4
26.
Use the explicit formula An=4.8 + (n − 1)2
to find the 11th term in the described arithmetic sequence.
(1 point)
A11 =
Question 5
27.
Manuel has saved $253.32 so far. He plans to put $50 into his savings each month for the next year. How much money will Manuel have after a year of savings?
(1 point)
$
Question 6
28.
Use the table to answer the question.
The sequences for the two functions is shown in the table. Which of the following statements are true?
(1 point)
Responses
None of the above
None of the above
While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).
While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
Question 7
29..
Consider the sequence 41, 29, 17, 5...
The recursive function is ________ with A1 =
____.
(1 point)
Responses
An= An−1+12, 53
An= An−1+12, 53
An= An−1−12, 41
An= An−1−12, 41
An= 12An−1, −12
An= 12An−1, −12
Question 8
30.
Which function represents exponential decay?
(1 point)
Responses
y = .8 (3)x
y = .8 (3)x
y = 3 (4 )x
y = 3 (4 )x
y = 3(.5)x
y = 3(.5)x
y = 2(1.5)x
y = 2(1.5)x
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A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5000 wasps, the situation can be modeled by which equation?
(1 point)
Responses
w(t) = 5000(13)t
where w(t) is the number of wasps after t months
w(t) = 5000(13)t
where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months
w(t) = 5000(87)t
where w(t) is the number of wasps after t months
w(t) = 5000(87)t
where w(t) is the number of wasps after t months
w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
Question 2
24.
Which of the following statements is true about the above wasp equation?
(1 point)
Responses
As t increases, w increases slowly at first and then quickly
As t increases, w increases slowly at first and then quickly
As t increases, w increases quickly at first and then slowly
As t increases, w increases quickly at first and then slowly
As t increases, w decreases slowly at first and then quickly
As t increases, w decreases slowly at first and then quickly
As t increases, w decreases quickly at first and then slowly
As t increases, w decreases quickly at first and then slowly
Question 3
25.
Given the explicit formula for the sequence in function notation, find the 5th term of the sequence.
f(n) = 2n−1
(1 point)
f(5) =
Question 4
26.
Use the explicit formula An=4.8 + (n − 1)2
to find the 11th term in the described arithmetic sequence.
(1 point)
A11 =
Question 5
27.
Manuel has saved $253.32 so far. He plans to put $50 into his savings each month for the next year. How much money will Manuel have after a year of savings?
(1 point)
$
Question 6
28.
Use the table to answer the question.
The sequences for the two functions is shown in the table. Which of the following statements are true?
(1 point)
Responses
None of the above
None of the above
While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).
While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
Question 7
29..
Consider the sequence 41, 29, 17, 5...
The recursive function is ________ with A1 =
____.
(1 point)
Responses
An= An−1+12, 53
An= An−1+12, 53
An= An−1−12, 41
An= An−1−12, 41
An= 12An−1, −12
An= 12An−1, −12
Question 8
30.
Which function represents exponential decay?
(1 point)
Responses
y = .8 (3)x
y = .8 (3)x
y = 3 (4 )x
y = 3 (4 )x
y = 3(.5)x
y = 3(.5)x
y = 2(1.5)x
y = 2(1.5)x
Skip to navigation
Answers
GPT-4o mini
Let's go through each question one by one.
**Question 1:**
You are asked to model the growth of a wasp nest with an exponential growth rate of 13% per month and a current population of 5000 wasps.
The correct model for exponentially growing populations is given by the formula:
\[ w(t) = P \cdot (1 + r)^t \]
where:
- \( P \) is the initial population,
- \( r \) is the growth rate,
- \( t \) is time in months.
Given that \( P = 5000 \) and \( r = 0.13 \) (13% as a decimal), the correct equation is:
\[ w(t) = 5000(1.13)^t \]
So, the answer is:
**w(t) = 5000(1.13)t where w(t) is the number of wasps after t months.**
**Question 2:**
You are asked about the behavior of the function \( w(t) \) over time.
Since it is an exponential growth function, as \( t \) increases, \( w(t) \) will increase slowly at first and then more rapidly. Thus, the statement that is true is:
**As t increases, w increases slowly at first and then quickly.**
**Question 3:**
You are given the function \( f(n) = 2n - 1 \) and asked to find the 5th term.
To find the 5th term:
\[ f(5) = 2(5) - 1 = 10 - 1 = 9 \]
So, the answer is:
**f(5) = 9.**
**Question 4:**
You are given the explicit formula \( A_n = 4.8 + (n - 1)2 \) and asked to find the 11th term.
To find the 11th term:
\[ A_{11} = 4.8 + (11 - 1) \cdot 2 = 4.8 + 10 \cdot 2 = 4.8 + 20 = 24.8 \]
So, the answer is:
**A11 = 24.8.**
**Question 5:**
Manuel starts with $253.32 and adds $50 each month for a year (12 months).
Amount saved after a year:
\[ 253.32 + (50 \times 12) = 253.32 + 600 = 853.32 \]
So, the answer is:
**$853.32.**
**Question 6:**
This question refers to the growth rates of two functions based on a table not provided. However, typically in this context, the answer about growth rates might depend on initial comparisons or trends. Assuming standard behavior for exponential growth, the second option seems plausible.
Without the specific table, I would assume:
**While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).**
**Question 7:**
You need a recursive function for the sequence 41, 29, 17, 5...
The sequence shows a decrease of 12 at each step:
- From 41 to 29: -12
- From 29 to 17: -12
- From 17 to 5: -12
Thus, the recursive formula is:
**An = An−1 − 12, A1 = 41.**
**Question 8:**
To determine which function represents exponential decay, check the base of the exponent. If the base is less than 1, it indicates decay.
The options have:
- \( y = .8(3)^x \) (grows)
- \( y = 3(4)^x \) (grows)
- \( y = 3(0.5)^x \) (decays)
- \( y = 2(1.5)^x \) (grows)
Thus, the answer is:
**y = 3(0.5)^x.**
Please confirm the logic or provide any missing context if necessary!
**Question 1:**
You are asked to model the growth of a wasp nest with an exponential growth rate of 13% per month and a current population of 5000 wasps.
The correct model for exponentially growing populations is given by the formula:
\[ w(t) = P \cdot (1 + r)^t \]
where:
- \( P \) is the initial population,
- \( r \) is the growth rate,
- \( t \) is time in months.
Given that \( P = 5000 \) and \( r = 0.13 \) (13% as a decimal), the correct equation is:
\[ w(t) = 5000(1.13)^t \]
So, the answer is:
**w(t) = 5000(1.13)t where w(t) is the number of wasps after t months.**
**Question 2:**
You are asked about the behavior of the function \( w(t) \) over time.
Since it is an exponential growth function, as \( t \) increases, \( w(t) \) will increase slowly at first and then more rapidly. Thus, the statement that is true is:
**As t increases, w increases slowly at first and then quickly.**
**Question 3:**
You are given the function \( f(n) = 2n - 1 \) and asked to find the 5th term.
To find the 5th term:
\[ f(5) = 2(5) - 1 = 10 - 1 = 9 \]
So, the answer is:
**f(5) = 9.**
**Question 4:**
You are given the explicit formula \( A_n = 4.8 + (n - 1)2 \) and asked to find the 11th term.
To find the 11th term:
\[ A_{11} = 4.8 + (11 - 1) \cdot 2 = 4.8 + 10 \cdot 2 = 4.8 + 20 = 24.8 \]
So, the answer is:
**A11 = 24.8.**
**Question 5:**
Manuel starts with $253.32 and adds $50 each month for a year (12 months).
Amount saved after a year:
\[ 253.32 + (50 \times 12) = 253.32 + 600 = 853.32 \]
So, the answer is:
**$853.32.**
**Question 6:**
This question refers to the growth rates of two functions based on a table not provided. However, typically in this context, the answer about growth rates might depend on initial comparisons or trends. Assuming standard behavior for exponential growth, the second option seems plausible.
Without the specific table, I would assume:
**While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).**
**Question 7:**
You need a recursive function for the sequence 41, 29, 17, 5...
The sequence shows a decrease of 12 at each step:
- From 41 to 29: -12
- From 29 to 17: -12
- From 17 to 5: -12
Thus, the recursive formula is:
**An = An−1 − 12, A1 = 41.**
**Question 8:**
To determine which function represents exponential decay, check the base of the exponent. If the base is less than 1, it indicates decay.
The options have:
- \( y = .8(3)^x \) (grows)
- \( y = 3(4)^x \) (grows)
- \( y = 3(0.5)^x \) (decays)
- \( y = 2(1.5)^x \) (grows)
Thus, the answer is:
**y = 3(0.5)^x.**
Please confirm the logic or provide any missing context if necessary!