1 Multiple Choice 5 points Youinvested \( \$ 1500 \) into an account with an annual percentage rate of \( 6 \% \) compounded annually. You plan to keep the money in the account for the next 10 years. Consider the function that relates the time and the amount of money in the account. Which is the most appropriate domain? \[ \begin{array}{l}x \geq 0 \\ 0 \leq x \leq 10 \\ y \geq 1500 \\ 1500 \leq x \leq 2686\end{array} \]

To determine the most appropriate domain for the function that relates time (\( x \)) to the amount of money (\( y \)) in the account, let's analyze the given scenario: - **Initial Investment:** \( \$1500 \) - **Annual Interest Rate:** \( 6\% \) compounded annually - **Investment Duration:** 10 years ### Understanding the Variables: - **\( x \)** represents the time in years. - **\( y \)** represents the amount of money in the account after \( x \) years. ### Analyzing the Options: 1. **\( x \geq 0 \):** - This implies that time can be any non-negative value, extending indefinitely into the future. - **Not appropriate** because the investment is planned for a specific duration of 10 years. 2. **\( 0 \leq x \leq 10 \):** - This restricts time to the period from the start (0 years) up to 10 years. - **Appropriate** as it aligns with the investment duration. 3. **\( y \geq 1500 \):** - This describes the range of the function, indicating that the amount will be at least the initial investment. - **Not the domain**, so it's irrelevant for this question. 4. **\( 1500 \leq x \leq 2686 \):** - This incorrectly assigns monetary values to \( x \), which represents time. - **Incorrect** because \( x \) should represent time, not money. ### Conclusion: The most appropriate domain for the function is the one that restricts \( x \) to the investment period of 10 years. **Answer:** \( 0 \leq x \leq 10 \)