Und noch eine kleine Herausforderung für die klugen Köpfe.
A water tank is designed with a horizontal base. At time t minutes, the depth of water in the tank is x cm. When t = 0, x = 72. In the side of the tank there is a tap which the water can flow through. When the tap is opened, the flow of water is modelled by the differential equation.
dx / dt = -4(x-8)^{1/3}
The owner of the tank needs to drain it to a depth of 35cm for maintenance. How long (in minutes) does it take for the level of water to fall from a depth of 72cm to the desired depth?
