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)=80+(n−1)100
f left parenthesis n right parenthesis equals 80 plus left parenthesis n minus 1 right parenthesis 100

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)=100+(n−1)80

Answer 1

To model the situation described, note the initial deposit of $100 at Roy's first birthday and the subsequent annual deposits of $80 starting from his second birthday. We can derive the model step-by-step.

1. At Roy's first birthday (n=1), the account balance is $100.
2. At Roy's second birthday (n=2), the account balance becomes $100 + $80 = $180.
3. At Roy's third birthday (n=3), the account balance is $100 + $80 + $80 = $260.
4. At Roy's fourth birthday (n=4), the account balance becomes $100 + $80 + $80 + $80 = $340.

From this, we can see that the total amount in the account after \( n \) years can be expressed as:

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

Here, \( 100 \) is the initial deposit, and \( 80 \times (n - 1) \) accounts for the additional deposits starting after the first year.

Thus, the correct function that models the situation is:

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

So, the correct option is:

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