A bottle of water is taken out of a refrigerator. The temperature of the water in the bottle is 4°C. The bottle water is taken outside to drink. The air temperature outside is constant at 24°C.

It is given that the rate at which the water in the bottle warms up is proportional to the difference in the air temperature outside and the temperature of the water in the bottle.

After 2 minutes the temperature of the water in the bottle is 11°C.

a. How long does it take for the water to warm 20°C ?

b. According to the model, what temperature will the water in the bottle eventually reach if the air temperature remains constant and the water is not drunk?