A problem on population growth

We consider a special case of the non-linear population growth model, with recursive relation. We try to achieve a formula for this model with mathematical analysis calculations.Assume that b is a positive constant. Also, consider that s 0 is the basic reproduction. Let:Pt+1 = sPt 1 + bPt be a recursive relation for a non-linear population growth model, then: Pm = (s − 1)s mPo (s − 1) + b(sm − 1)P0 .