A heater for a semiconductor wafer has first order dynamics, with the following transfer function relating changes in temperature T to changes in the heater input power P : P(s)T(s)=s+1K where K has units of C/kW and has units of minutes. The process is at steady-state when an engineer changes the power input stepwise from 1 to 2 kW. They note the following: - The process temperature initially is 100C and steady. - Four minutes after changing the power input, the temperature is 400C. - Thirty minutes later, the temperature is 500C and steady. a. What is the gain of the process? b. What is the time constant of the process