Step 1:

The population modeled differential equation is .

(a)

Find values of  for which population is increasing.

Population is increasing when .

and

and

and

Population is increasing for .

Step 2:

(b)

Find values of  for which population is decreasing.

Population is decreasing when .

and

and

Population can never be negative, is not considered.

Population is decreasing for .

Step 3:

(c)

Find Equilibrium solutions.

Equilibrium occurs when .

and

and

and

Equilibrium solutions are or .

Solution:

(a) Population is increasing for .

(b) Population is decreasing for .

(c) Equilibrium solutions are or .