Problem-8 (25 Points) The following model is a cooling system where the thermostat q switches on when the temperature is above 78°F and switches off at 72°F = RC T-Rq+ Ta(t) T(0) = 75°F Tis room air temperature in F Ta(t)=90+10sin() outside air temp in F t is in hours q=9*105 lb-ft/hr the input from cooling system R =6*10-5 (°F) (hr)/lb thermal resistance C = 3*104 lb-ft/ °F thermal capacitance Determine how much energy is used (the integral of q over time is the energy used) over a 24 hour time period