QuestionAn air conditioner cools a home when the outside temperature is about 78 EdegF. During the summer you can model the outside temperature in degrees Fahrenheit using the function $f(t)=72-9 \cos \left(\frac{1}{12} \pi t\right)$ where $t$ is the number of hours past midnight. During what hours is the air conditioner cooling the home? Round the hour to nearest tenth.
Time format is a 24 hour clock, please pay attention to notes beside answer boxes (for auto-grading purposes).
The air conditioner comes on approximately $\square$ hours after midnight or $\square$ A.M. (enter answer as h:mm *do not put a zero in front of the hour for answers like: 3:25, do NOT enter as 03:25)
By the symmetry of the graph, it goes off about $\square$ hours before midnight or $\square$ P.M. (enter answer as hh:mm *for an answer like 7:15 pm enter using 24 hour format as: 19:15)