Hospitals aren't carrying over any food when a new citizen is born. My understanding is that if it requires 150 food for a new citizen, with a hospital, 75 food is carried over when a new citizen is born. However, what I'm seeing is nothing of the sort. In fact, it told me that I had two turns till a new citizen was born. I had +8 food, and I require 155 food for a new citizen. I hit next turn and my city had grown. I'm now at 11.25 / 155 food. I'm guessing it actually means 50% of current food intake, which seems insanely worthless. A whole 4 extra food. Wow.