An important model for commercial fisheries is that of Beverton and Holt. It begins with t study of a single cohort of fish- that is, all the fish in the study are born at the same time. a cohort of the North Sea plaice (a type of flatfish), the number N "Non of fish in th population is given N=1000e^-0.1t

t = 15.18 years old

B(t) = 6,320*e^-0.1t*( 1 - 0.93*e^ -0.095t )^3]

t = 13.426 years

Step-by-step explanation:

The complete question is given as follows:

Given:

- The number of fish in population according to bio-mass:

                             N = 1000*e^-0.1t

- The weight of each fish is given by:

                             w = 6.32*( 1 - 0.93*e^ -0.095t )^3

w : Weight in pounds,

t : Age in years

Find:

- If a fish weighs 3 pounds, how old is it?

- Find the Formula for biomass B(t) = w*N , and graph the function.

- At what age is the bio-mass largest?

Solution:

- Using the weight formula and set w = 3 , we have:

                               3 = 6.32*( 1 - 0.93*e^ -0.095t )^3

                               e^ -0.095t = (1 - ∛(3/6.32))/0.93

                              -0.095*t = Ln | (1 - ∛(3/6.32)) / 0.93 |

                               t = -Ln | (1 - ∛(3/6.32)) / 0.93 | / 0.095

                               t = 15.18 years old

- The Bio-mass function is given by the product of total number N fishes and the weight of each fish w.

                              B(t) = [ 1000*e^-0.1t ]*[6.32*( 1 - 0.93*e^ -0.095t )^3]

                              B(t) = 6,320*e^-0.1t*( 1 - 0.93*e^ -0.095t )^3]

- The graph is plotted as attached.

- From the plotted graph the function B(t) maximizes when t = 13.426 years

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