Chapter 2.5, Problem 85AYU

85. Thermostat Control Energy conservation experts estimate that homeowners can save $\text{5\%}$ to $\text{10\%}$ on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the graph (next page), 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 $y\text{ = }T\left(t\right)-\text{ 2}$. Explain how this affects the temperature in the house. Graph this new function.

(c) The homeowner reprograms the thermostat to $y\text{ = }T\left(t\text{ + 1}\right)$. Explain how this affects the temperature in the house. Graph this new function.

Source: Roger Albright, 547 Ways to Be Fuel Smart, 2000