Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation $\frac{dT}{dt} = k(T - A)$, where $T$ is the temperature of the object after $t$ units of time have passed, $A$ is the ambient temperature of the object's surroundings, and $k$ is a constant of proportionality.
Suppose that a cup of coffee begins at 180 degrees and, after sitting in room temperature of 63 degrees for 12 minutes, the coffee reaches 174 degrees. How long will it take before the coffee reaches 161 degrees?
Include at least 2 decimal places in your answer.
