The average length in centimetres of a channel catfish (species ictalurus punctatus) at age t years is estimated by the von Bertalanffy growth model L() - GLACI - 0.76- 15) L(d) (em) 2 4 6 8 10 12 14 16 18 20 (a) Calculate the average length (in centimetres) of a channel catfish at age t = 7 years. Provide your answer to 3 decimal places in the box below: [1 mark] (b) Consider the following three models: In 0,71 Model 1: (() = -0.15 In L 610(1-0.74) Model 2: 1(D) = -0.15 In -L GLOXO.74 Model 3: t() = -0.15 The model which predicts the average age t (in years) of a channel catfish of length L (in centimetres) is . [2 marks] (c) Find the age * (in years) at which the model predicts a channel catfish will each a length of 54 cm. Provide your answer to 3 decimal places in the box below: [1 mark] years (d) What is the value of the parameter Is. which denotes the upper bound to growth? (This will be the horizontal asymptote value for L().) Provide your answer to 2 decimal places in the box below: [1 mark] cmIt is known that the von Bertalanffy growth model L(t) = A(1 - Be-rt ) satisfies the informal differential equation Growth rate of L(t) = r(A - L(t)). In this question, we verify this fact for a specific value of t. Suppose the von Bertalanffy growth model is defined by the constants A = 240, B = 0.7, P = 2.5, that is, L(t) = 240(1 - 0.7e-2.5t) (a) Calculate the central difference approximation (CDA) of the function L(t) with h = 0.01 fort = 2. [2 marks] (b) Calculate the central difference approximation (CDA) of the function L(t) with h = 0.001 fort = 2. [2 marks] (c) Calculate the right-hand side of the informal differential equation (1) for t = 2 [2 marks]