Mrs. Varner deposited \( q \) dollars in a bank account that has been earning annual interest. The total value of the account is based on the function \( f(x)=q \cdot 1.025^{x} \), where \( x \) represents the number of years the money has been in the account. If no deposits or withdrawals are made after the initial deposit, which equation represents the total value of the account 5 years from now? \( f(x)=q \cdot 1.025^{x}+5 \) \( f(x)=q \cdot 1.025^{x+5} \) \( f(x)=q \cdot 1.025^{x-5} \) \( f(x)=q \cdot 1.025^{x}-5 \)

To determine the total value of Mrs. Varner's bank account **5 years from now**, we'll analyze the given function and the provided options. ### **Given:** - **Initial Deposit:** \( q \) dollars - **Interest Rate:** 2.5% annually (since \( 1.025 \) represents a 2.5% increase each year) - **Function for Account Value:** \( f(x) = q \cdot 1.025^{x} \), where \( x \) is the number of years the money has been in the account. ### **Objective:** Find the equation that represents the **total value** of the account **5 years from now**. ### **Approach:** 1. **Understand the Function:** - The function \( f(x) = q \cdot 1.025^{x} \) gives the account balance after \( x \) years. 2. **5 Years from Now:** - To find the balance **5 years from now**, we essentially want to evaluate what the account balance will be at \( x + 5 \) years. - This means we substitute \( x \) with \( x + 5 \) in the original function to get the future value. 3. **Modify the Function:** - \( f(x + 5) = q \cdot 1.025^{x + 5} \) ### **Reviewing the Options:** 1. **\( f(x) = q \cdot 1.025^{x} + 5 \):** - **Incorrect.** This adds 5 dollars to the current balance, which doesn't account for compound interest over 5 years. 2. **\( f(x) = q \cdot 1.025^{x+5} \):** - **Correct.** This correctly adjusts the exponent to account for the additional 5 years of compound interest. 3. **\( f(x) = q \cdot 1.025^{x-5} \):** - **Incorrect.** This subtracts 5 years, implying looking back in time, which is not relevant for future value. 4. **\( f(x) = q \cdot 1.025^{x} - 5 \):** - **Incorrect.** This subtracts 5 dollars from the current balance, which doesn't align with the growth due to interest. ### **Conclusion:** The correct equation that represents the total value of the account **5 years from now** is: \[ f(x) = q \cdot 1.025^{x + 5} \] **Answer:** \( f(x)=q \cdot 1.025^{x+5} \)