I'm coming up with a fictional world but I want to make accurate population projections. I'm trying to model population growth where the rate of growth is inversely proportional to the population density. I can calculate it for very small periods of time, tried doing days in Google Sheets but it crashed after a few million cells. I figure the answer is probably a diffeq or integral or something I never got to in my singular year of college. Basically I want an equation where P1 is expressed in terms of t. P0 and a are already known.