To model the relationship between the number of months \( x \) and the total amount of money \( y \) in Oliwia's account, we start with the initial deposit and then account for the interest earned over time.
- Initial Deposit: Oliwia deposits $3,000. This is the starting point for the function.
- Interest Earned: The account earns $3 in interest each month. Therefore, after \( x \) months, the total interest earned will be \( 3x \).
The total amount of money in the account after \( x \) months can be expressed as:
\[ y = 3000 + 3x \]
This equation shows that the total amount \( y \) is the initial deposit of $3,000 plus the interest earned over \( x \) months.
Now, if we rearrange the equation to fit the standard form of a linear function, it becomes:
\[ y = 3x + 3000 \]
So, the correct equation that models the relationship between the number of months and the total amount of money Oliwia will have in her account is:
\[ y = 3x + 3000, \text{ where } x \text{ is the number of months and } y \text{ is the total amount of money.} \]
Thus, the correct response from the options given 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.
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