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.

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.
Responses

f(n)=80+(n−1)100

f(n)=80(100)n−1

f(n)=100+(n−1)80

f(n)=100+80(n)

GPT-4o mini · Answer

To model the situation where Roy's grandfather deposits money into the bank account, we can analyze the deposits and how they accumulate over the years.

On Roy's first birthday (n=1), the initial deposit is $100.
On each subsequent birthday (from n=2 onward), he deposits an additional $80.

Thus, the total balance on Roy's nth birthday can be calculated as:

For n=1 (first birthday): $100$
For n=2 (second birthday): $100 + 80 = 180$
For n=3 (third birthday): $100 + 80 + 80 = 260$
For n=4 (fourth birthday): $100 + 80 + 80 + 80 = 340$

We can see that after the first birthday, there are $n-1$ deposits of $80. So, the overall expression for the balance on the nth birthday can be modeled as:

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

This simplifies to:

\[ f(n) = 100 + 80n - 80 = 80n + 20 \]

However, in the options provided, we want to select the one that matches our formula:

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

This matches the understanding that the balance on Roy's nth birthday is $100 plus $80 for each subsequent year after the first.