The level in a tank responds as a first-order system to changes in its inlet flow. The data shown below were gathered after the inlet flow was increased quickly from 1.5 to 4.8 gal/min.
(a) Determine the transfer function by estimating the time constant using one of the methods of Section 7.2. Be sure to use deviation variables and include units for the model parameters.
(b) Repeat part (a) using nonlinear regression (e.g., Excel) and the liquid level data.

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Table E7.8 Time (min) Level Level Time (ft) (min) (ft) 0.00 10.4 1.75 20.3 0.25 12.0 2.00 21.5 0.50 13.5 2.25 22.1 0.75 15.1 2.50 22.9 23.7 1.00 16.8 2.75 1.25 18.1 30.7 (steady state) 1.50 19.2 15.0