Wikipedia has the formula for the
Verhulst equation that is the standard one used for population growth.
There are two constants, K (the carrying capacity) and r (the growth rate).
K signifies the maximum number of individuals that the enivronment will allow (due to limite resources like food and space).
r signifies the speed of population growth (how many offspring are produced).
Ecologists define K species as those that have a steady population size, with few offspring and usually a long lfe span (like elephants), while r species have fluctuating populations and large numbers of offspring, like ruderal weeds (e.g. poppies) or fruit-flies.
The model species you describe is probably a K species, so I'd start with a high K (possibly a few hundred thousand if you modelling global population) and a low r (I don't know, how about 0.01?).
Herbie