a problem on population growth

We consider a special case of the non-linear population growth model, withrecursive relation. we try to achieve a formula for this model with mathematical analysiscalculations.assume that b is a positive constant. also, consider that s > 0 is the basic reproduction. let:pt+1 =spt1 + bptbe a recursive relation for a non-linear population growth model, then:pm =(s − 1)smpo(s − 1) + b(sm − 1)p0.