Newtoon's law of cooling with a variable ambient temperature (a) suppose a body is heated to 90 f and placed in a room held at constant temperature of 70°f aer oné hour the temperature of the body is 82°f find a fonction that represents the temperature of the body at time t. graph this function and note its relation to the constant ambient temperature. (b) suppose now that the temperature in the room is 70°f when the body is place in it, but decreasing linearly at a rate of 5 each hour. replace the constant ambient temperature in newton's law of cooling with the appropriate linear function of t. suppose that the temperature of the body after one hour in the room is 76°f. express the temperature of the as a function of time. use maple to determine the proportionality constant. graph the temperature function of the body and the temperature of the room on same set of axes. (c) make a conjecture about the behavior of the temperature of the body in relation to the room temperature. verify your conjecture analytically.