A single-tank process has been operating for a long period of time with the inlet flow rate q_i equal to 30.1 ft³/min. After the operator increases the flow rate suddenly at t = 0 by 10%, the liquid level in the tank changes as shown in Table E7.2. Assuming that the process dynamics can be described by a first-order model, calculate the steady-state gain and the time
constant using three methods: 

(a) From the time required for the output to reach 63.2% of the total change.
(b) From the initial slope of the response curve. 

(c) From the slope of the fraction incomplete response curve.
(d) Compare the data and the three models by simulating their step responses.

Table E7.2 (min) (ft) (min) (ft) 5.50 1.4 6.37 0.2 5.75 1.6 6.40 1.8 0.4 5.93 6.43 0.6 6.07 2.0 6.45 0.8 6.18 3.0 6.50 1.0 6.26 4.0 6.51 1.2 6.32 5.0 6.52