The von Bertalanffy growth model is used to predict the length L(t) of a fish over a period of time. If L∞ is the largest length for a species, then the hypothesis is that the rate of growth in length is proportional to L∞ – L, the length yet to be achieved.
(a) Formulate and solve a differential equation to find an expression for L (t).
(b) For the North Sea haddock it has been determined that L∞ = 53cm, L (0) = 10, cm, and the constant of proportionality is 0.2. What does the expression for L (t) become with these data?