According to Newton’s Law of Cooling, the rate at which a hot object cools down depends on certain factors, including the physical properties of the object and the difference between the object’s temperature and the surrounding temperature. The author poured hot water into a ceramic cup and measured its temperature as it cooled down in a $65^{\circ}$ room. Using Newton’s Law of Cooling, a formula was found to model the temperature (in degrees Fahrenheit) of the cup over time (measured in minutes): $$T = f(t) = 65 + 100.7e^{-0.042t}$$

1. What was the starting temperature of the cup?
   Answer: degrees
2. According to the equation, what will be the temperature of the cup at $120$ seconds?
   Answer: degrees
3. According to the equation, when will the temperature of the cup be $106^{\circ}\text{?}$ Answer this by using properties of logarithms to solve an equation. Give your answer correct to at least $3$ decimal places.
   Answer: