Question

In a population of lions, the proportionate death rate is 0.55 per year and the

proportionate birth rate is 0.45 per year. Formulate a model of the population. Solve

the model and discuss its long term behavior. Also, find the equilibrium point of the

model.

Answer 1

Let B be the birth rate=0.45/year

and D be the death rate =0.55/year

Let N be the Population size of Model

Then Rate of propulation Growth

$$\dfrac{dN}{dt}=\text {Birt rate - Death rate}=B-D$$

$$\dfrac{dN}{dt}=0.45-0.55=-0.1/year<0$$

Natural growth decay equation:

$$\dfrac{dN}{dt}=-0.1N$$

Solve the equation

$$N(t)=N(0)e^{-0.1t}$$

where $N(0)$ is the population at time $t=0.$

$N(t)\to0$ as $t\to \infin.$

Since $-0.1N\not=0$ for $t\geq0,$ then there are no equlibrium points.