Derivatives and Their Applications · Paper 3 — Free Maths AI HL Practice Questions

A water tank has a rectangular base of area $20\,\text{m}^2$. Water flows into the tank at a constant rate of $3\,\text{m}^3$ per minute. At time $t$ minutes, the depth of water in the tank is $h$ metres. The tank has a small leak at its base; water leaks out a rate proportional to the depth, so that the net rate of change of volume $V$ (in $\text{m}^3$) satisfies $$\frac{dV}{dt} = 3 - kh$$ where $k$ is a positive constant.