Indices and Measures of Natural Increase

Abstract

In the case of a Malthusian population annual births increase or decrease according to the same “compound interest rate” r as the population, so that

$$\left. {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\frac{{B(t)}}{{B(t - x)}}}&{ = {e^{rx}}} \end{array}}\\ { = R_0^{x/T}} \end{array}} \right\}$$

(244)

this formula being valid for every value of x.