What are the equilibrium solutions?

Question

A population is modeled by the differential equation

(a) For what values of P is the population increasing?

(b) For what values of P is the population decreasing?

(c) What are the equilibrium solutions?

Answer 1

Step 1:

(a)

The population modeled differential equation is .

Find values of  for which population is increasing.

Population is increasing when .

and

and

and

Population is increasing for .

Solution:

(a) Population is increasing for .

Answer 2

Step 1:

(b)

The population modeled differential equation is .

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 .

Solution:

(b) Population is decreasing for .

Answer 3

Step 1:

(c)

The population modeled differential equation is .

Find Equilibrium solutions.

Equilibrium occurs when .

and

and

and

Equilibrium solutions are or .

Solution:

(c) Equilibrium solutions are or .