The system below consists of a header tank of constant cross-sectional area of 0.36m? that is filled with lubricating oil. The tank is designed to feed the turbocharger of a large diesel engine in the case of a power black-out. The tank must provide oil to the turbocharger to prevent damage during its emergency shut-down which takes approximately 10 seconds. In order to maintain oil pressure to the turbocharger the oil must not drop below a height of 10cm during these 10 seconds. OIL IN OIL OUT (a) Form a differential equation that represents the system. (b) Solve the differential equation given that h = h, at t = 0. %3D (c) Determine the time it will take for the tank to reach the minimum level of 10cm if the initial height of oil, h, is 50cm and k = 0.05, plot a graph of h against and hence decide if the tank is suitable.