Modeling Pollution in a River?

📌 CONCEPT: The problem of modeling pollution in a river can be solved using the concept of integration, where the total amount of pollutants is calculated by integrating the concentration of pollutants along the length of the river.

📐 RULE / FORMULA: To find the total amount of pollutants, we can use the formula for the area under a linear curve, which is given by the equation: Area = (1/2) × (base) × (height).

💡 WORKED EXAMPLE: Let's say the river is 10 km long, with the concentration of pollutants being 4 kg/m at the source and 2 kg/m at the point of discharge. We can treat this as a linear equation, where the concentration decreases by 2 kg/m over a distance of 10 km. Using the formula, we can calculate the total amount of pollutants as: Total amount = (1/2) × 10 × (4 + 2) = 30 kg.

⚠️ COMMON MISTAKE: Students often forget to consider the base and height of the area under the curve, leading to incorrect calculations. It's essential to understand that the base represents the length of the river, and the height represents the concentration of pollutants.