Classify the systems as linear or nonlinear systems, and time-varying or time-invariant systems, where x(t) and y(t) represent the input and output, respectively: [a] y(t) = 0.2x(t - 1) [b] y(t) = tx(t) [c] y(t) = x(t) + t [d] y(t) = x(t) + 1 [e] y(t) = x(t) cos (t)

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.