1. A heater for a semiconductor wafer has first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is P(s)T(s)=s+1K where K has units [C/Kw ] and has units [min]. The process is at steady state when an engineer changes the power input stepwise from 1 to 2kW. She notes the following: (i) The process temperature initilly is 100C. (ii) Four minutes after changing the power input, the temperature is 400C. (iii) Thirty minutes later the temperature is 500C. (a) What are K and t in the process transfer function? (b) If at another time the engineer changes the power input linearly at a rate of 0.5kW/min, what can you say about the maximum rate of change of process temperature: When will it occur? How large will it be