What will happen if a pregnant rabbit is put in a small fenced farm, with plenty of food. This rabbit will be left for years.
If the rabbits have unlimited food (and presumably water), the limiting factor on how many you will eventually have will be space; in other words, you will end up with as many rabbits as can fit on your small farm. There is a good reason for the cliche "breeding like rabbits". Rabbits are very fertile and prolific. But let's look at your question with specific numbers.
Your pregnant female will give birth within the month to a litter of between one and fourteen babies. Technically the mother could get pregnant again within minutes of giving birth, but she will have to wait until one of her male babies is old enough to impregnate her. If the mother has all female babies you are done--no more rabbits other than the initial litter. If there is even one male, when it reaches sexual maturity at six months the population will start to take off. All the female rabbits then will begin to have litters every month. The numbers grow rapidly. The link below supposes a low number scenario of three females per litter and then calculates the numbers. After two years, you would have over 2,000 rabbits. After four years, the number reaches close to four million rabbits! If you have a large enough farm, after seven years (the average life span of a rabbit) you could have over 180 *billion* rabbits!