Question
Wren decided to save some money in the first week, $2 in the second week, $3 in the third week, and so forth. The sequence 1, 2, 3, 4, 5, . . . indicates the amounts Wren set aside each week. Create a function model for this situation.(1 point)
Responses
f(n)=1n−1
f left parenthesis n right parenthesis equals 1 superscript n minus 1 baseline
f(n)=1+(n−1)
f left parenthesis n right parenthesis equals 1 plus left parenthesis n minus 1 right parenthesis
f(n)=n−1
f left parenthesis n right parenthesis equals n minus 1
f(n)=2n−1
Responses
f(n)=1n−1
f left parenthesis n right parenthesis equals 1 superscript n minus 1 baseline
f(n)=1+(n−1)
f left parenthesis n right parenthesis equals 1 plus left parenthesis n minus 1 right parenthesis
f(n)=n−1
f left parenthesis n right parenthesis equals n minus 1
f(n)=2n−1
Answers
GPT-4o mini
In this scenario, Wren saves an amount of money that increases by $1 each week, starting at $1 in the first week. Therefore, the amount saved in the nth week can be represented as follows:
1. In the 1st week, Wren saves $1.
2. In the 2nd week, Wren saves $2.
3. In the 3rd week, Wren saves $3.
4. Continuing this pattern, in the nth week, Wren saves $n.
This leads us to conclude that the function \( f(n) \), which represents the amount saved in the nth week, is simply:
\[ f(n) = n \]
Given the options provided, the closest one that represents this scenario correctly is:
**None of the options provided exactly represent \( f(n) = n \).**
If we review the provided options:
- \( f(n) = 1n−1 \) (not correct)
- \( f(n) = 1 + (n−1) \) (simplifies to \( n \), but not clear)
- \( f(n) = n−1 \) (incorrect, would give $0 in the first week)
- \( f(n) = 2n−1 \) (this implies an incorrect starting point)
Based on the interpretations, the best fit within the context of the logic is actually linked to the option **\( f(n) = 1 + (n-1) \)**, as it evaluates to \( f(n) = n \).
So the correct response can be effectively considered as:
\[ f(n) = 1 + (n−1) \] (simplifies to \( f(n) = n \)).
1. In the 1st week, Wren saves $1.
2. In the 2nd week, Wren saves $2.
3. In the 3rd week, Wren saves $3.
4. Continuing this pattern, in the nth week, Wren saves $n.
This leads us to conclude that the function \( f(n) \), which represents the amount saved in the nth week, is simply:
\[ f(n) = n \]
Given the options provided, the closest one that represents this scenario correctly is:
**None of the options provided exactly represent \( f(n) = n \).**
If we review the provided options:
- \( f(n) = 1n−1 \) (not correct)
- \( f(n) = 1 + (n−1) \) (simplifies to \( n \), but not clear)
- \( f(n) = n−1 \) (incorrect, would give $0 in the first week)
- \( f(n) = 2n−1 \) (this implies an incorrect starting point)
Based on the interpretations, the best fit within the context of the logic is actually linked to the option **\( f(n) = 1 + (n-1) \)**, as it evaluates to \( f(n) = n \).
So the correct response can be effectively considered as:
\[ f(n) = 1 + (n−1) \] (simplifies to \( f(n) = n \)).