Sketch the level response for a bathtub with cross-sectional area of 8ft2 as a function of time for the following sequence of events; assume an initial level of 0.5ft with the drain open. The inflow and outflow are initially equal to 2ft3/min (a) The drain is suddenly closed, and the inflow remains con- stantfor 3min(0t3). (b) The drain is opened for 15 min; assume a time constant in a linear transfer function of 3min, so a steady state is essentially reached ( 3t18) (c) The inflow rate is doubled for 6min(18t 24). (d) The inflow rate is returned to its original value for 16min(24t40)