Given the Logistic growth function F(X)=rX (1-2), the Gompertz growth function F(X) = TXIn (), and...

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Given the Logistic growth function F(X)=rX (1-2), the Gompertz growth function F(X) = TXIn (), and the Shaefer (Catch per Unit Effort) production function Y = H(E,X) = qEX a) Derive the expression for biomass (X) at steady state equilibrium for Logistic and Gompertz growth functions, respectively. b) Derive the Yield-Effort functions for the two growth functions. c) If the Gompertz yield-effort function and the Logistic Yield effort function attain maximum sustainable yields (MSY) at (E = 100) and (E = 50), calculate the MSYS for the two function for the values of (q=0.005), (r=0.5) and carrying capacity (K = 200). Given the Logistic growth function F(X)=rX (1-2), the Gompertz growth function F(X) = TXIn (), and the Shaefer (Catch per Unit Effort) production function Y = H(E,X) = qEX a) Derive the expression for biomass (X) at steady state equilibrium for Logistic and Gompertz growth functions, respectively. b) Derive the Yield-Effort functions for the two growth functions. c) If the Gompertz yield-effort function and the Logistic Yield effort function attain maximum sustainable yields (MSY) at (E = 100) and (E = 50), calculate the MSYS for the two function for the values of (q=0.005), (r=0.5) and carrying capacity (K = 200).

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a Steady state equilibrium for Logistic and Gompertz growth functions The steady state equilibrium for a growth function is the point where the growth ... View the full answer