In the month of January, a cerlain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of \( 48 \% \) per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell this year? \( \sum_{n=0}^{11}(1.048)^{n}(9,000) \) \( \sum_{n=1}^{12}(1.048)^{n}(9,000) \) \( \sum_{n=1}^{12}(4.8 n+9,000) \) \( \sum_{n=0}^{12} 4.8 n+9,000 \)

To determine the number of burgers the restaurant expects to sell over the next year with a **48% monthly growth rate**, we need to use an exponential growth formula. Here's a step-by-step explanation: 1. **Initial Sales**: In January, the restaurant sold **9,000 burgers**. 2. **Growth Rate**: Sales are expected to grow at **48% per month**. This means each subsequent month, the sales are multiplied by **1.48** (since 48% growth translates to multiplying by 1 + 0.48). 3. **Exponential Growth Formula**: The number of burgers sold each month can be represented as: \[ \text{Sales in month } n = 9,000 \times (1.48)^n \] where \( n \) starts from **0** (for January) and goes up to **11** (for December). 4. **Total Sales Over the Year**: To find the total number of burgers sold over the entire year, you sum the sales for each month: \[ \sum_{n=0}^{11} 9,000 \times (1.48)^n \] However, looking at the provided options, there's a slight discrepancy in the growth rate factor (1.048 instead of 1.48). Assuming this is a typo and should represent 48% growth, the closest and correct structure is: \[ \sum_{n=0}^{11} (1.048)^n \times 9,000 \] **Correct Option:** \[ \sum_{n=0}^{11} (1.048)^{n}(9,000) \] Answer: \[ \sum_{n=0}^{11}(1.048)^{n}(9,000) \]