1. **Problem statement:** Estimate the company's profit if 7800 cars are sold, based on the given data points for cars sold (in thousands) and profit (in millions). 2. **Given data:** Cars sold (thousands): 6, 7, 8, 9, 10 Profit (millions): 4, 6, 8, 8, ? 3. **Step 1: Understand the problem** We want to estimate profit for 7.8 thousand cars sold (7800 cars). Since 7.8 is between 7 and 8, we will use interpolation between points (7,6) and (8,8). 4. **Step 2: Use linear interpolation formula** The formula for linear interpolation between points $(x_1,y_1)$ and $(x_2,y_2)$ at $x$ is: $$y = y_1 + \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)$$ 5. **Step 3: Substitute values** Here, $x_1=7$, $y_1=6$, $x_2=8$, $y_2=8$, and $x=7.8$. $$y = 6 + \frac{8 - 6}{8 - 7} (7.8 - 7) = 6 + 2 \times 0.8 = 6 + 1.6 = 7.6$$ 6. **Step 4: Conclusion** The estimated profit when 7800 cars are sold is **7.6 million dollars**.