(1 point) newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. suppose that the temperature of a cup of coffee obeys newton's law of cooling. let k > o be the constant of proportionality. assume the coffee has a temperature of 205 degrees fahrenheit when freshly poured, and 3 minutes later has cooled to 188 degrees in a room at 74 degrees (a) write an initial value problem for the temperature t of the coffee, in fahrenheit, at time t in minutes. your answer will contain the uknown constant k: t(0) = (b) solve the initial value problem in part (a). your answer will contain the unknown constant ke t(t) = (c) determine the value of the constant k ke (d) determine when the coffee reaches a temperature of 148 degrees * minutes