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 0.5 ft with the drain open. The inflow and outflow are initially equal to 2ft³ /min.
(a) The drain is suddenly closed, and the inflow remains constant for 3 min (0 ≤ t ≤ 3).
(b) The drain is opened for 15 min; assume a time constant in linear transfer function of 3 min, so a steady state is essentially reached (3 ≤ t ≤ 18).

(c) The inflow rate is doubled for 6 min (18 ≤ t ≤ 24).
(d) The inflow rate is returned to its original value for 16 min (24 ≤ t ≤ 40).