Question
A) 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)
f(n) = n − 1
f(n) = 1
n − 1
f(n) = 1 + (n − 1)
f(n) = 2n − 1
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)
f(n) = n − 1
f(n) = 1
n − 1
f(n) = 1 + (n − 1)
f(n) = 2n − 1
Answers
GPT-4o mini
The amounts Wren sets aside each week can be represented by the sequence 1, 2, 3, 4, 5, ..., which corresponds to the week number. Specifically, for week \( n \), Wren saves \( n \) dollars.
In this case, the function \( f(n) \) that represents the amount saved in week \( n \) can be expressed as:
\[ f(n) = n \]
This means that for each week number \( n \), Wren saves exactly \( n \) dollars.
From your answer options, the most appropriate function that fits this description is:
\[ f(n) = n \]
However, if \( f(n) = 1 + (n - 1) \) is also listed as an option, it simplifies to \( f(n) = n \), so it is also correct.
Thus, the correct function model for the amount Wren saves each week is:
1. \( f(n) = n \) (Ideal).
2. \( f(n) = 1 + (n - 1) \) (Also acceptable since it simplifies to \( f(n) = n \)).
In this case, the function \( f(n) \) that represents the amount saved in week \( n \) can be expressed as:
\[ f(n) = n \]
This means that for each week number \( n \), Wren saves exactly \( n \) dollars.
From your answer options, the most appropriate function that fits this description is:
\[ f(n) = n \]
However, if \( f(n) = 1 + (n - 1) \) is also listed as an option, it simplifies to \( f(n) = n \), so it is also correct.
Thus, the correct function model for the amount Wren saves each week is:
1. \( f(n) = n \) (Ideal).
2. \( f(n) = 1 + (n - 1) \) (Also acceptable since it simplifies to \( f(n) = n \)).