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+80(n) f left parenthesis n right parenthesis equals 100 plus 80 left parenthesis n right parenthesis 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)=100+(n−1)80 f left parenthesis n right parenthesis equals 100 plus left parenthesis n minus 1 right parenthesis 80 f(n)=80+(n−1)100
Answers
GPT-4o mini
To model the situation described, we need to create a function \( f(n) \) that represents the total balance in the bank account on Roy's \( n \)-th birthday.
1. On Roy's first birthday (when \( n = 1 \)), his grandfather deposits $100.
2. On each subsequent birthday (starting from the second birthday onwards), his grandfather deposits $80.
This results in the following balances:
- For \( n = 1 \): \( f(1) = 100 \)
- For \( n = 2 \): \( f(2) = 100 + 80 = 180 \)
- For \( n = 3 \): \( f(3) = 180 + 80 = 260 \)
- For \( n = 4 \): \( f(4) = 260 + 80 = 340 \)
From this pattern, we can build the function. The first deposit is $100, and from the second birthday onward, each year contributes an additional $80. Hence, the function can be represented as:
\[
f(n) = 100 + (n - 1) \times 80
\]
This means that for every birthday \( n \), starting from 1, we add $100 and then $80 multiplied by the number of additional years (which is \( n - 1 \)).
Thus, the correct answer among the provided options is:
\[
f(n) = 100 + (n - 1) \times 80
\]
1. On Roy's first birthday (when \( n = 1 \)), his grandfather deposits $100.
2. On each subsequent birthday (starting from the second birthday onwards), his grandfather deposits $80.
This results in the following balances:
- For \( n = 1 \): \( f(1) = 100 \)
- For \( n = 2 \): \( f(2) = 100 + 80 = 180 \)
- For \( n = 3 \): \( f(3) = 180 + 80 = 260 \)
- For \( n = 4 \): \( f(4) = 260 + 80 = 340 \)
From this pattern, we can build the function. The first deposit is $100, and from the second birthday onward, each year contributes an additional $80. Hence, the function can be represented as:
\[
f(n) = 100 + (n - 1) \times 80
\]
This means that for every birthday \( n \), starting from 1, we add $100 and then $80 multiplied by the number of additional years (which is \( n - 1 \)).
Thus, the correct answer among the provided options is:
\[
f(n) = 100 + (n - 1) \times 80
\]