A wildlife biologist surveyed the manatee population in Blue Springs State Park in 2009. He observed 326 manatees during that visit. He returned to the park each year since and found that, on average, there were 11 fewer manatees. 1. What are the quantities that are changing in this scenario? 2. Define the variables \( m \) and \( y \). 3. What is the parameter? 4. What is the constant? 5. Which equation represents this scenario? \[ \begin{array}{ll} \square & m=326 y-11 \\ \square & m=-11 y+326 \\ \\ & y=326-11 m \\ \end{array} \]

Let's address each of your questions step by step based on the given scenario. ### 1. **Quantities That Are Changing** - **Number of Manatees**: This is the primary quantity that is changing over time. - **Time (Years Since 2009)**: As each year passes, the number of manatees decreases. ### 2. **Defining the Variables \( m \) and \( y \)** - **\( m \)**: Represents the **number of manatees** in Blue Springs State Park. - **\( y \)**: Represents the **number of years** since 2009. ### 3. **Parameter** - The **parameter** in this scenario is the **rate at which the manatee population decreases each year**, which is **11 manatees per year**. ### 4. **Constant** - The **constant** is the **initial number of manatees** observed in 2009, which is **326 manatees**. ### 5. **Equation Representing the Scenario** The correct equation that models the situation is: \[ m = -11y + 326 \] **Explanation:** - **\( m \)** decreases by **11** for each additional year (**\( y \)**), starting from **326**. - This aligns with the format \( m = \text{(slope)} \times y + \text{(y-intercept)} \), where the slope is negative, indicating a decrease. The other provided equations do not correctly represent the relationship described in the scenario. --- **Summary of Answers:** 1. **Changing Quantities**: Number of manatees and number of years since 2009. 2. **Variables Defined**: - \( m \): Number of manatees. - \( y \): Number of years since 2009. 3. **Parameter**: The average decrease of 11 manatees per year. 4. **Constant**: The initial number of manatees, 326. 5. **Correct Equation**: \[ m = -11y + 326 \]