Aleksei lives in Yakutsk--- the coldest inhabited city in the world where the average temperature goes down to as low as -50 oC during winter. Yakutsk is built on permafrost, and it is not uncommon to find whole bodies of preserved mammoths should one dig into the ground. One Christmas day, while Aleksei was trying to design an arch in the shape of an inverted catenary, his home heating decided to stop working. Fortunately (or not) Newton’s law of cooling still works. So here goes the problem you need to solve: (a) At 9 AM, the temperature inside Aleksei’s house was 20 oC. Two hours later, the temperature inside his house was 15.5 oC. The ambient temperature on that day was -60 oC. Find k for his house. (b) At what time will the temperature drop to zero? (c) Aleksei’s dad who holds a doctor’s degree in physics and serves as director of Russia’s Permafrost Engineering Institute arrived from work at 7 PM and was able to fix the heater at 9 PM. After 2 h, the room temperature was 5 oC. At what time will their house temperature go back to 20 oC? (Assume that the ambient temperature remained at -60 oC).

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