Breeding like rabbits...
I hate to be pedantic (well, no I don't), but the reproductive capacity of rabbits isn't nearly as impressive as most people think. A female rabbit in good condition can produce a litter of 4-10 kittens every 30 days. In optimal conditions, they can do this for 8-9 months of the year, so potentially one female could produce close to a hundred offspring in one year. Young females can produce their first litter at 4 or 5 months, so it is possible for a female to produce grandchildren in one season.
In practice, the breeding rate is much lower than that (except in certain parts of Australia). The point that most people miss, though, is that 90% or more of rabbit offspring will never see their first birthday, due to predation and disease. The rate of population increase for rabbits is still pretty good for a mammal, but not nearly as explosive as people imagine.
So yes, the 4000 escaped rabbits may well be able to produce, say 10,000 offspring in a few weeks, but most of those will be dead by the end of the year anyway...