Unit step response data are given in Table E7.15 for a process with gain K = 2. Fit the data to a first order model with no time delay. Next use linear regression to fit a first-order discrete-time equation to the data with Δt = 1. Then plot the predicted value of y(t) for both models and compare with the data in Table E7.15. Calculate the gain of the discrete-time model and compare with the known value of K = 1. Why are the two values different?

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Table E7.15 Time y(t) 0.0 0.05 0.22 3 0.37 0.47 4 0.58 0.68 0.77 0.82 9. 0.87 10 0.90