I do think that it's safe to say the floor is at $3k as demonstrated by this chart, and anywhere below that wouldn't be sustainable at this point because there has been so many new investors and corporations that have been made aware of bitcoin in the 2017 bull run that would drive demand for cheap coins.
Bitcoin has always been fundamentally sound but we are seeing a real shift in sentiment I think which is the underlying cause of the rallies, people aren't as uncertain about the market as they were last year, and psychology had a lot to do with it.
We could see an incoming correction due to the fact that prices have risen so consistently over the past weeks, potentially down below $5k as I don't think there is sufficient support there yet. It's only natural that this happens, as price corrections are a matter of time in such instances. But in the medium to long term I think this should be the start of a bull market, and the halving next year will only further the bullishness.