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Rate-of-growth model for biological organisms

$$\begin{array}{rcl} \frac{ d l }{ dt } & = & K \cdot \left(L - l\right) \\ \end{array}$$
Variable Type Description Value (default) Datatype
\(K\) parameter growth rate \(\) Real
\(L\) parameter asymptotic final length (L infinity) \(\) Real
\(l\) free length \(\) Real

The Bertalanffy equation is an equation that describes the rate of growth of a biological organism. The equation was offered by Ludwig von Bertalanffy in 1969.


Integrating the equation gives:

$$ l = L (1 - e^{-Kt}) $$


The body of this page comes from Wikipedia.


Bertalanffy, L. von, (1969). General System Theory. New York: George Braziller, pp. 136

Modelica Code

model VonBertalanffyGrowth
  "Rate-of-growth model for biological organisms"
  parameter Real K "growth rate";
  parameter Real L "asymptotic final length (L infinity)";
  Real l "length";
  der(l) = (K * (L - l));
end VonBertalanffyGrowth;

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