[Increase functions of the type dW/dt=ktp(E-W)n and their integrals (author's transl)].
In 2 previous papers increase functions of the v. Bertalanffy (1941) type dW/dt = kWm (En--Wn) and a modified form dW/dt = kWm (E--W)n were treated, both yielding a variety of integrals resp. growth functions, most of them reaching the final value W = E after infinite time. Now an ansatz with better integration conditions dW/dt = ktp (E--W)n is presented implying t also on the right side of the basic equation and giving only two types of growth functions determined by n = 1 or 0 less than n less than 1. In the first case there appears a slightly generalized Janoschek (1957) growth function with W leads to E for t leads to infinity but a rather good position of the turning point, i.e. the abscissa of maximum increase. In the second case the result is a growth function with a definite time to reach adultness, thus being better suited to natural conditions. Graphs show the flexibility of the 2 solutions and their increase functions, including an example for practical application.
D006128:Growth; D008954:Models, Biological
Zuwachsfuktionen vom Typ dW/dt=ktp(E-W)n und ihre Integrale.