Why is it that a container of warm water in a refrigerator cools down faster than a container of cold water?

Answer

The rate of cooling is proportional to the difference in temperature between the container of water and the air in the refrigerator. So the cooling is also slower and slower, as that difference gets smaller and smaller, to fall back to zero when the water and air in the refrigerator have reached the same temperature. Note that that air has also become a bit warmer (except that the cooling must have kicked in by now to compensate)!