To derive the equation that models the total amount of money in Oliwia's bank account over time, we start with the initial deposit amount and account for the monthly interest.
- Initial Deposit: Oliwia deposits $3,000.
- Monthly Interest: The account earns $3 in interest per month.
Let \( x \) be the number of months. The total amount of money, \( y \), in the account after \( x \) months can be expressed as:
\[ y = \text{initial deposit} + \text{(interest per month)} \times \text{(number of months)} \]
Substituting the values we have:
\[ y = 3,000 + 3x \]
Thus, the equation of the linear function that models the relationship between the number of months \( x \) and the total amount of money \( y \) in her account is:
\[ y = 3x + 3,000 \]
So the correct response is:
y = 3x + 3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.