Final answer:
The relationship between the number of months and Alice's savings is best described by option d, which is f(n) = 2,000 + 150(n - 1), accounting for her initial savings and monthly contributions.
Step-by-step explanation:
The correct answer is option d which is f(n) = 2,000 + 150(n - 1). Alice starts her savings with $2,000 and plans to add $150 each month. The function that describes the relationship between the number of months (n) and her account's balance (f(n)) adds $150 for each month that passes, but since she already has $2,000 in the account to begin with, that amount doesn't need to be multiplied. When n = 1 (the first month), she will not add another $150 since she starts with $2,000, so we subtract 1 from n to adjust for this in the formula.
The function that describes the relationship between the number of months that pass (n) and the balance of Alice's savings account (f(n)) is a linear function. The initial balance in Alice's savings account is $2,000, and she contributes $150 each month. The amount contributed each month is subtracted from the initial balance. Therefore, the function is f(n) = 2,000 - 150n, where n represents the number of months that have passed.
For example, after 1 month, the balance in Alice's savings account will be 2,000 - 150(1) = $1,850. After 2 months, the balance will be 2,000 - 150(2) = $1,700, and so on.