(Solution) - The von Bertalanffy growth model is used to predict the length -(2025 Original AI-Free Solution)

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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?