Question: A cup of coffee is heated to 100 degrees Centigrade at t = 0 minutes. The cup is placed in a refrigerator which is kept constant at 0 degrees Centigrade. Let u(t) denote the temperature of the coffee after t minutes.

a) Obtain the correct expression for u(t) by solving an appropriate differential equation.

b) If the temperature of the coffee is 80 degrees after 1 minute, find out how long it will take for the coffee to cool down to 10 degrees.