To create a function that models the situation described, we need to account for the initial deposit of $100 on Roy's first birthday and the $80 increments that follow for each year thereafter.
Given:
- On Roy's first birthday (n=1), the amount in the account is $100.
- On Roy's second birthday (n=2), the account balance becomes $100 + $80 = $180.
- On the third birthday (n=3), the balance is $100 + $80 + $80 = $260.
- On the fourth birthday (n=4), the balance is $100 + $80 + $80 + $80 = $340.
The pattern shows that the balance can be modeled with a function that includes the initial deposit and the linear accumulation of $80 for each passing year after the first.
The balance function can be represented as:
- For the first year (n=1), \( f(1) = 100 \)
- For the second year (n=2), \( f(2) = 100 + 80 \times 1 = 180 \)
- For the third year (n=3), \( f(3) = 100 + 80 \times 2 = 260 \)
- For the fourth year (n=4), \( f(4) = 100 + 80 \times 3 = 340 \)
We can generalize this into a function: \[ f(n) = 100 + 80(n - 1) \] This can also be written equivalently as: \[ f(n) = 100 + 80n - 80 = 80n + 20 \]
However, the first option provided in your responses matches perfectly with the sequence for the years after the first year: \[ f(n) = 100 + 80(n - 1) \]
So, the correct function that models this situation is: \[ f(n) = 100 + 80(n - 1) \]
This is the response you would select from the options you've given.