**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.