The population model differential equation is .

(a) Find the constant solutions of the equation.

The constant solutions of the equation occurs when .

and

and

and

and

, and .

The constant solutions of the equation are , and .

(b) Find the values of  is increasing.

increasing when .

.

for all values of .

, and ,

and or and

or .

  is increasing for  or .

is increasing for .

(c) Find the values of  is decreasing.

increasing when .

.

for all values of .

and

.

is decreasing for .

(a) The constant solutions of the equation are , and .

(b) is increasing for .

(c) is decreasing for .