$\"\"$

\

(a)

\

Population $\"\"$ satisfies the differential equation $\"\"$ , $\"\"$ .

\

Rewrite the logistic equation as

\

$\"\"$

\

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

\

Compare above equation with $\"\"$ .

\

Therefore, $\"\"$ and $\"\"$ .

\

Carrying capacity is $\"\"$ .

\

$\"\"$

\

(b) Find $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(c)

\

$\"\"$ .

\

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

\

Where $\"\"$ .

\

Here $\"\"$ .

\

$\"\"$

\

Find the time when the population reaches $\"\"$ of the carrying capacity.

\

Therefore, $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Population reaches $\"\"$ of the carrying capacity after $\"\"$ years.

\

$\"\"$

\

(a) Carrying capacity is $\"\"$ .

\

(b) $\"\"$ .

\

(c) Population reaches $\"\"$ of the carrying capacity after $\"\"$ years.