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4) + fit. Suppose we argue that the growth rate per person is proportional to the difference between the food available and the food consumed. Then we have dP -1 _ - a(F(0) + j t - P). , /l= 0), this is the logistic model of Verhulst (1844). 5) as the generalized logistic model. 7) gives some promise from a curve fitting standpoint. 8) P(t) x F(0) + Pt. For a long established society, we might expect the Malthusian argument would yield a population that tracks the supposedly linear growth of the food supply.
That is, it would simply have been so troublesome to iterate the recursion formula 120 times that it would have been worth our while to go through the algebra required to bring things to a more manageable procedure for finding Plzo. Just to give the reader a bit of feel for the relative cognitive utility of the recursion relation and the hazards of seeking a closed form solution, we shall demonstrate two methods for obtaining a closed form solution. 42. 79(1+ s + sZ + ... 791 -s This is a fine way to proceed.
There are an infinite number of models that will do this. It will be hard for us to choose among them. Consequently, we here borrow a maxim from the Radical Pragmatist William of Occam and try to pick a simple model that is consistent with Malthus’ conjecture and with the facts before us. 24) otherwise. 3, it appears that population growth is close to log-linear until around 1860. 24) is t* = 1860. 029648. 49954. 57879 k * We still must estimate F(0). In this case, we shall guess that a value around 10 will be close to the truth.