Question
On Roy’s first birthday, his grandfather placed $100 in a bank account. On Roy’s second birthday, his grandfather placed $80 in the account and continued to place $80 each passing year. The arithmetic sequence 100, 180, 260, 340,… indicates the account balance for the first four years. Create a function that models this situation.(1 point)
Responses
f(n)=100+(n−1)80
f left parenthesis n right parenthesis equals 100 plus left parenthesis n minus 1 right parenthesis 80
f(n)=80(100)^n−1
f left parenthesis n right parenthesis equals 80 left parenthesis 100 right parenthesis superscript n minus 1 baseline
f(n)=80+(n−1)100
f left parenthesis n right parenthesis equals 80 plus left parenthesis n minus 1 right parenthesis 100
f(n)=100+80(n)
Responses
f(n)=100+(n−1)80
f left parenthesis n right parenthesis equals 100 plus left parenthesis n minus 1 right parenthesis 80
f(n)=80(100)^n−1
f left parenthesis n right parenthesis equals 80 left parenthesis 100 right parenthesis superscript n minus 1 baseline
f(n)=80+(n−1)100
f left parenthesis n right parenthesis equals 80 plus left parenthesis n minus 1 right parenthesis 100
f(n)=100+80(n)
Answers
GPT-4o mini
To model the situation described, we see that Roy's grandfather deposits $100 on Roy's first birthday and $80 for each subsequent birthday after that.
The account balance can be written as follows:
- On Roy's first birthday (n=1), the balance is $100.
- On Roy's second birthday (n=2), the balance is $100 + $80 = $180.
- On Roy's third birthday (n=3), the balance is $100 + $80 + $80 = $260.
- On Roy's fourth birthday (n=4), the balance is $100 + $80 + $80 + $80 = $340.
You can see that each year after the first, an additional $80 is added. Therefore, the total amount after n years can be modeled by the following function:
\( f(n) = 100 + 80(n - 1) \)
Where:
- \( 100 \) is the initial deposit at n=1.
- \( 80(n - 1) \) accounts for the $80 deposited for each year after the first.
Thus, the correct function that models this situation is:
**f(n) = 100 + (n - 1) * 80**
So the correct answer is:
**f(n) = 100 + (n−1)80**
The account balance can be written as follows:
- On Roy's first birthday (n=1), the balance is $100.
- On Roy's second birthday (n=2), the balance is $100 + $80 = $180.
- On Roy's third birthday (n=3), the balance is $100 + $80 + $80 = $260.
- On Roy's fourth birthday (n=4), the balance is $100 + $80 + $80 + $80 = $340.
You can see that each year after the first, an additional $80 is added. Therefore, the total amount after n years can be modeled by the following function:
\( f(n) = 100 + 80(n - 1) \)
Where:
- \( 100 \) is the initial deposit at n=1.
- \( 80(n - 1) \) accounts for the $80 deposited for each year after the first.
Thus, the correct function that models this situation is:
**f(n) = 100 + (n - 1) * 80**
So the correct answer is:
**f(n) = 100 + (n−1)80**