Problem 7. A cup of soup is initially poured into a cup at t = 0 minutes at 190° F. Suppose that it cools to 180°F in 1 minute in a room with a (constant) ambient temperature of 90° F. (a) (b) (c) Assume that Newton's law of heating/cooling applies-that is, the rate of change of the temperature is proportional to the difference in its temperature and that of the environment. Write an initial-value problem that models the temperature of the soup as a function of time, and box your answer. Solve to find an exact equation for the temperature soup at an unknown time t. Box your answer. How long does it take for the soup to reach a temperature of 110°F?