Consider the growth of a population p t It starts out with p 0 A Suppose the growth is unchecked and hence p kp for some constant k Then p t Of course populations don t grow forever Let s say there is a stable population size Q that p t approaches as time passes Thus the speed at which the population is growing will approach zero as the population size approaches Q One way to model this is via the differential equation p kp Qp p 0 A The solution of this initial value problem is p t