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)

Question

Responses

f(n)=100+80(n)
f left parenthesis n right parenthesis equals 100 plus 80 left parenthesis n right parenthesis

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+(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

Answer 1

To model the account balance based on the information provided, we need to consider how the deposits are made over the years.

1. On Roy's first birthday (when \( n = 1 \)), his grandfather deposits $100.
2. On his second birthday (when \( n = 2 \)), he deposits $80.
3. Every year after that, for each subsequent birthday, another $80 is deposited.

From the information, we can see that after \( n \) years, the amount deposited can be calculated as follows:

• For \( n = 1 \): $100 (only the first deposit)
• For \( n = 2 \): $100 + $80 (the first and second deposits = $180)
• For \( n = 3 \): $100 + $80 + $80 (the first and first two deposits + second deposit = $260)
• For \( n = 4 \): $100 + $80 + $80 + $80 (the first deposit + three years of $80 = $340)

This gives us the total balance as:

\[ f(n) = 100 + 80(n - 1) \]

where \( n \) is the year of Roy's age.

So the correct function that models this scenario is:

\[ f(n) = 100 + 80(n - 1) \]

Thus, the correct response is:

f(n) = 100 + 80(n - 1)

In function notation, this would read as:

f left parenthesis n right parenthesis equals 100 plus 80 left parenthesis n minus 1 right parenthesis.