$\"\"$

\

Pacific halibut fishery has been modeled by the differential equation $\"\"$

\

Logistic differential equation with carrying capacity $\"\"$ is $\"\"$ .

\

Solution of the logistic differential equation $\"\"$ is $\"\"$ ,

\

Where $\"\"$ .

\

As the differential equation $\"\"$ is similar to $\"\"$ .

\

Solution of the differential equation $\"\"$ is $\"\"$ .

\

Where $\"\"$ .

\

(a)

\

Here $\"\"$ per year and $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Find the biomass after one year $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in the above expression.

\

$\"\"$

\

Biomass after one year is $\"\"$ kg.

\

$\"\"$

\

(b)

\

Find the time when the biomass reaches $\"\"$ kg.

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Biomass reaches $\"\"$ when $\"\"$ .

\

$\"\"$

\

(a)

\

Biomass after one year is $\"\"$ .

\

(b)

\

Biomass reaches $\"\"$ when $\"\"$ .