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

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

f(n)=100+(n−1)80

GPT-4o mini · Answer

To develop a function that models the account balance for Roy from his first birthday onward, let’s analyze the deposits:

On Roy's first birthday, $100 is deposited.
On his second birthday, $80 is deposited.
Thereafter, $80 is deposited each year.

This creates a pattern where the total balance at age $ n $ can be expressed as:

For $ n = 1 $: $ f(1) = 100 $
For $ n = 2 $: $ f(2) = 100 + 80 = 180 $
For $ n = 3 $: $ f(3) = 100 + 80 + 80 = 260 $
For $ n = 4 $: $ f(4) = 100 + 80 + 80 + 80 = 340 $

From this, we see that each year after the first, an additional $80 is added. The formula can be structured as follows:

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

Here, $ n - 1 $ accounts for the additional years after the first birthday.

So, the correct function is:

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

Thus, the response that matches this is:

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