Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called to the phone for last minute arrangements, and his coffee is forgotten. When he finally returns to his coffee 35 minutes later, the temperature had been decreasing by 1.2% per minute.

Question

Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park.  The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C.  Mr. Currie was called to the phone for last minute arrangements, and his coffee is forgotten.  When he finally returns to his coffee 35 minutes later, the temperature had been decreasing by 1.2% per minute.

a)	What type of function best models the cooling of a hot liquid? 
         Explain your choice.

b)	What is the mathematical model for this situation? (i.e. - the equation)

c)	If the optimal temperature for drinking a hot liquid is 280C, at what time 
         would Mr. Currie have had to return in order to enjoy his cup of coffee?