This simple model demonstrates logistic growth.The differential equation looks like
where K is the carrying capacity of the quantity y. Alternatively,
y'(t)=by(t) - b/K*y(t)^2
so the growth term suggests exponential growth, but there is a loss term is of the form b/K y(t) -- loss is proportional to population (crowding).
A comparable Mathematica file is available at http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/LogisticGrowth-and-DecayModel.nb