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
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).
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.
None of the above
None of the above
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
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
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).
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.
None of the above
None of the above
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
Answers
GPT-4o mini
Here are the answers to each of your questions:
### Question 1:
**Modeling the Wasp Growth**
The exponential growth of the wasp population can be modeled by the equation:
**w(t) = 5000(1.13)^t**
Where w(t) is the number of wasps after t months.
### Question 2:
**Behavior of Wasp Growth Equation**
The correct statement regarding the growth of the wasp population is:
**As t increases, w increases slowly at first and then quickly.**
This reflects the nature of exponential growth.
### Question 3:
**Finding the 5th Term**
Given the function f(n) = 2n−1, we find:
f(5) = 2(5)−1 = 2(5) - 1 = 10 - 1 = **9**.
### Question 4:
**Finding the 11th Term of Arithmetic Sequence**
Using the formula An = 4.8 + (n − 1)2 to find the 11th term:
A11 = 4.8 + (11 − 1)2
A11 = 4.8 + (10)2
A11 = 4.8 + 100 = **104.8**.
### Question 5:
**Total Savings after a Year**
Starting with $253.32 and adding $50 each month for 12 months:
Total savings = $253.32 + $50 * 12 = $253.32 + $600 = **$853.32**.
### Question 6:
**Understanding Growth Rates in Functions**
If we have two functions with specified growth rates, the appropriate true statement could be:
**While the growth rate of g(x) is initially greater than 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:
**Recursive Function of the Sequence**
For the sequence 41, 29, 17, 5..., the recursive definition is:
**An = An−1 - 12, 41**.
A1 = 41.
### Question 8:
**Identifying Exponential Decay**
The function that represents exponential decay is:
**y = 3(0.5)^x**.
This is because it has a base (0.5) that is less than 1.
If you have more questions or need further explanations, feel free to ask!
### Question 1:
**Modeling the Wasp Growth**
The exponential growth of the wasp population can be modeled by the equation:
**w(t) = 5000(1.13)^t**
Where w(t) is the number of wasps after t months.
### Question 2:
**Behavior of Wasp Growth Equation**
The correct statement regarding the growth of the wasp population is:
**As t increases, w increases slowly at first and then quickly.**
This reflects the nature of exponential growth.
### Question 3:
**Finding the 5th Term**
Given the function f(n) = 2n−1, we find:
f(5) = 2(5)−1 = 2(5) - 1 = 10 - 1 = **9**.
### Question 4:
**Finding the 11th Term of Arithmetic Sequence**
Using the formula An = 4.8 + (n − 1)2 to find the 11th term:
A11 = 4.8 + (11 − 1)2
A11 = 4.8 + (10)2
A11 = 4.8 + 100 = **104.8**.
### Question 5:
**Total Savings after a Year**
Starting with $253.32 and adding $50 each month for 12 months:
Total savings = $253.32 + $50 * 12 = $253.32 + $600 = **$853.32**.
### Question 6:
**Understanding Growth Rates in Functions**
If we have two functions with specified growth rates, the appropriate true statement could be:
**While the growth rate of g(x) is initially greater than 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:
**Recursive Function of the Sequence**
For the sequence 41, 29, 17, 5..., the recursive definition is:
**An = An−1 - 12, 41**.
A1 = 41.
### Question 8:
**Identifying Exponential Decay**
The function that represents exponential decay is:
**y = 3(0.5)^x**.
This is because it has a base (0.5) that is less than 1.
If you have more questions or need further explanations, feel free to ask!