The population model differential equation is .

(a) Find values of  for which population is increasing.

Population is increasing when .

 and 

 and 

 and 

Population is increasing for .

(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 .

(c) Find Equilibrium solutions.

The population modeled differential equation is .

Equilibrium occurs when .

 and 

 and 

 and 

Equilibrium solutions are  or .

(a) Population is increasing for .

(b) Population is decreasing for .

(c) Equilibrium solutions are  or .