Tank Filling Problem?

📌 CONCEPT: The problem involves the application of integrals to model the rate of flow of water into the tank and calculate the time taken to fill it to a certain volume.

📐 RULE / FORMULA: We will use the formula for the volume of water in the tank, which is given by the integral of the rate of flow with respect to time, i.e., V = ∫(100 + 0.02V)dt, where V is the volume in litres.

💡 WORKED EXAMPLE: Let's consider an example where the tank is filled to 4800 litres. We need to find the time taken to fill the tank. We can model this situation using the given rate of flow and solve the integral to find the time taken.

⚠️ COMMON MISTAKE: Students often forget to consider the initial condition that the tank is initially empty, or they may incorrectly apply the integral to solve for the time taken, which can lead to incorrect answers.