Early in the film, Judy boards a train to Zootopia after being accepted into the police. On the way, we see a sign indicating you are leaving Bunnyburrow which includes a real time population counter.
This counter is about "081,435,816" (commas added for emphasis) which is ~81.4 million rabbits, and is increasing steadily. It appears to go from ...5810 to ...5816 in 2 seconds which is an increase of ~3 rabbits per second.
Even earlier in the film, her mom indicates Judy has "275 brothers and sisters". (!)
Also, based on the fact that she was scratched by Gideon when she was 9, and that she entered ZPD academy 15 years later, we can reasonably conclude she is at least 24 years old for most of the film. Although we don't have her parents' ages we can assume they are much older.
Finally, based on the advanced technology demonstrated, including medical technology as evidenced by the equipment in the hospital re-purposed by the wolves, we can assume a very low childhood mortality rate.
Given this information, how accurate is the rate of increase of the population counter for Bunnyburrow? If it isn't accurate, what would be a more realistic rate of change? Finally, can anyone attempt to estimate a "carrying capacity" for Bunnyburrow (which is implied to be a small rural area)?
You'll probably have to make some assumptions, but supporting with evidence from the film is preferable obviously.
And yes, I understand the rabbit population is played for laughs throughout the film, I still think it deserves analysis.