(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> 0k> 0 be the constant of proportionality. assume the coffee has a temperature of 190 degrees fahrenheit when freshly poured, and 33 minutes later has cooled to 180 degrees in a room at 68 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 : dtdt=equation editort(0)=equation editor(b) solve the initial value problem in part (a). your answer will contain the unknown constant k .t(t)=equation editor(c) determine the value of the constant kk=equation editorminutes.(d) determine when the coffee reaches a temperature of 150 degrees. equation editorminutes.