Energy conservation experts estimate that homeowners can save 5% to 10% on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the given graph, the temperature T (in degrees Fahrenheit) of a home is given as a function of time t (in hours after midnight) over a 24-hour period.

(a) At what temperature is the thermostat set during daytime hours? At what temperature is the thermostat set overnight?

(b) The homeowner reprograms the thermostat to y = T(t) €“ 2. Explain how this affects the temperature in the house. Graph this new function.

(c) The homeowner reprograms the thermostat to y = T(t + 1). Explain how this affects the temperature in the house. Graph this new function.

Transcribed Image Text:

TA 80 76 72 68 64 60 56 8 12 16 20 24 Time (hours after midnight) 4 Temperature (°F)