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Dr Shaw
has the foreign body removed from her body and leaves it in the medical room.
Later, at the end of movie, she revisits the room and
the alien has grown about ten times the size, with no obvious access to food or energy.
How did it grow so fast?
The creature was trapped in a fully-equipped automated medical suite, which was clearly intended to keep a certain elderly man alive for as long as possible. In order to achieve that goal, it would need to be able to perform any sort of surgery - and probably, the most likely sort of surgery would be organ transplantation.
So, that means there must have been at least two other things in the room, besides fun-sized painkillers and a guys-only autodoc: blood (or some futuristic substitute), and replacement organs. Given the age of the intended patient, I wouldn't be surprised if there were muscle and bone grafts available as well. Some blood would have been readily available from the operating chair itself - since if a patient starts bleeding out you want to have a transfusion available immediately - and the organs would have been in cold storage somewhere nearby.
There was probably enough biological material available in that room to rebuild a person three or four times over if necessary, and all the creature would have had to do is bang open walls until it found the stuff.
That is something not really disclosed in the films. The aliens are genetically wired to grow large and fast, like in Alien where Parker was telling the others:
"It was like a man it was - it was ... big -"
It is one of the reasons they are so dangerous, they seem to lack a child phase and go from babies to adults within a couple of hours or maybe less.
Cells may have cavities filled in with mostly water (vacuoles). They allow cells (so the whole organism) to become much larger feeding mostly on water, with no other food. Plant seedlings grow from the seeds this way during the early stages of germination.
Vacuoles are common in plants but can be found in the Earth animals and protists, while this is much less usual. We do not know the biology of the creature. If the water was available in some pipe or tap inside medical room (quite probable), maybe this has been enough.
This does not explain the exact reason in the movie, just wanted to point out that fast growth need not contradict the logic or reality.
