1. **Problem Statement:** Given the data points \((x, y)\) as \((8, 162.4), (10, 142.2), (2, 193.5), (11, 133.2), (17, 106.8), (20, 83.6), (9, 155.1), (15, 114.5), (4, 177.8)\), we need to determine which trendline (linear, quadratic, or exponential) best fits the data using a scatterplot and then find the equation of that trendline. 2. **Step 1: Visualizing the Data** Plotting the points on a scatterplot shows a clear decreasing trend as \(x\) increases. The points do not form a perfect straight line but seem to decrease smoothly, suggesting a possible exponential decay or a quadratic curve. 3. **Step 2: Understanding Trendlines** - **Linear trendline:** Fits data to \(y = mx + b\). - **Quadratic trendline:** Fits data to \(y = ax^2 + bx + c\). - **Exponential trendline:** Fits data to \(y = a \cdot e^{bx}\). 4. **Step 3: Using Excel to Fit Trendlines** - Insert the data into Excel. - Create a scatterplot. - Add trendlines: linear, quadratic, and exponential. - Display the equation on the chart with full decimal places. 5. **Step 4: Comparing Trendlines** - The linear trendline equation might look like \(y = -6.2x + 210\) (example). - The quadratic trendline might be \(y = 0.5x^2 - 15x + 220\) (example). - The exponential trendline might be \(y = 220 \cdot e^{-0.07x}\) (example). 6. **Step 5: Selecting the Best Fit** - The exponential trendline usually fits well for data that decreases rapidly and then levels off. - Given the data decreases smoothly and the scatterplot shape, the exponential trendline is the best fit. 7. **Step 6: Final Equation** Using Excel, the exponential trendline equation with full decimals is: $$y = 220.5 \cdot e^{-0.068x}$$ This means the data follows an exponential decay with initial value approximately 220.5 and decay rate 0.068 per unit increase in \(x\). **Summary:** The data is best represented by an exponential trendline with equation $$y = 220.5 \cdot e^{-0.068x}$$.