The momentum of population growth with time dependent net maternity function

The momentum of population growth problem of Keyfitz is generalized to contain a gradual change of the age-specific birth rate ro the level of bare replacement. Assuming a time dependence for the net maternity function of the form (formula: see text) R being the net reproductive rate, we show that for the Malthusian model the asymptotic birth rate is increased by exp (r/lambda), where r is the rate of increase of the population before t = 0. A numerical method for obtaining the asymptotic birth rate for a general net maternity function with the same time dependence is outlined.