logistisches Wachstum mit Differentialgleichung berechnen A3008

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Die Differenzialgleichung vom logistischen Wachstum lautet: f'(t)=k*f(t)*(G-f(t)). f'(t) ist die Zunahme (oder Abnahme) des Bestandes, G-f(t) heißt Sättigungsmanko und ist der Wert um welchen der Bestand noch zu- oder abnehmen kann (also die Differenz von Grenze und aktuellem Bestand). Damit sagt die Differenzialgleichung aus, dass die momentane Änderung des Bestands proportional zum zum aktuellen Bestand und zum Sättigungsmanko ist. Die Parameter „k“ und „G“ tauchen auch in der Funktionsgleichung auf und heißen: k=Wachstumsfaktor=Proportionalitätsfaktor, 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