2. The von Bertalanffy growth model is used to predict the length L(t) of a sh over a period of time. If LM is the largest length for a species, then the growth model states that the rate of growth in the length is proportional to the dierence its current length and the largest length. (a) For the North Sea haddock it has been determined the its largest length, LM = 53cm and its initial length is given by 15(0) = 10cm and its constant of proportionality is [12. Choose the di'erential equation that ts this given growth model with L{t) =length of sh at time t in years and the given constants for the partic- ular species i. % = .2L 1503} = 10 ii. % = 2(53 L) L03) = 10 iii. % = .2(t 53) 15(0) = 11] (b) Now, solve the differential equation that is appropriate for this scenario. Show your steps in solving to nd the function L(t). (c) Suppose you catch a North Sea haddock this season (Spring 2022) and it is 10 cm long but the wildlife regulations state you can't keep a fish under 35 cm in length. Use your model to predict when you can legally catch and keep this sh