Question

Using the concept of a net rate introduced in Problem 2, determine a differential equation governing a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t.

Answer 1

We may be thinking about either of these choices depending on whether we are talking about immigration or emigration.

$\frac{d P}{d t}=r_g \pm r$

This is further explained below.

What is a differential equation?

Generally, The rates of births and deaths will be represented accordingly by the superscripts $r_b$ and $r_d$.

The model transforms into the following when subjected to the circumstances outlined in the problem:

$\frac{d P}{d t}=r_b P-r_d P^2$

In conclusion, You need to submit model 1 in order to get more information.

In the event that the proportionality assumptions about birth and death be loosened up, the model that is necessary for issue 1 would become the following:

$\frac{d P}{d t}=r_g \pm r$

Depending on whether we are discussing immigration or emigration, we may be contemplating either of these options.

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