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

f(n)=80+(n−1)100

Answer 1

To create a function that models the situation of Roy's bank account, we can break down the deposits made by his grandfather:

1. At Roy's first birthday (when \( n = 1 \)), there is an initial deposit of $100.
2. Each subsequent year (from \( n = 2 \) onwards), there is a deposit of $80.

The total amount in the account after \( n \) years can be expressed as:

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

Where:
- \( 100 \) is the initial deposit made on his first birthday.
- \( 80(n - 1) \) accounts for the $80 deposits made from the second year onward.

So the correct response is:

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

This matches the first option provided:

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