Unfortunately sponges like these don't last too long in home aquaria most of the time. They should be rated as very difficult IMO. This is due to a number of factors. Inside the sponge lives all kinds of life forms, tiny little crabs, shrimp and others. They must be acclimated extremely carefully and slowly to preserve this life. Then they need pristine water quality that has lots of phyto plankton and micro zoo plankton to feed on. And they can not be overcome with algae growth. Then the biggie - they have a very negative reaction to the shed nematocysts of corals, zoos and anemones in the tightly confined quaters of our tanks. Next biggie - they do not tolerate modification made with kalkwasser and many additives. Even a very small change in dKh (alkalinity) will have serious consequences sooner or later. In order to keep that from happening, small water changes would be done often as oppossed to one 20% change per month. Occassionally someone manages to keep one for quite some time and see it grow a lot, but this is due the habits of that particular aquarist, their salt mix and technique combined with feeding efforts for that tank. Short exposure to air will only cause some temporary effects, not long term if everything else is right. I just started a micro nano for sponges only. I have 3 sponges or sponge like animals in there. A blue one, a black one and a meat colored one. They are growing! I feed them from my phyto culture every day. This is good since I love sponges. If this works, then a large sponge tank is in order! For yours, you can cut the tips, but, if you get the conditions right, those tips will quickly regrow if left alone.