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A city block has 6 pigeons and then 1 week later there are 9 pigeons. Let P(t)be the number of pigeons where t is measured in weeks.

Assuming the growth continues proportionally, at the same rate, what is the differential equation which describes the growth of the pigeon population?

Answer :

Using proportions, it is found that the differential equation which describes the growth of the pigeon population is given by:

[tex]\frac{dP}{dt} = 1.5P[/tex]

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the initial population and the population one week later, the rate of growth is given by:

k = 9/6 = 1.5.

The standard differential equation for population growth is:

[tex]\frac{dP}{dt} = kP[/tex]

Hence:

[tex]\frac{dP}{dt} = 1.5P[/tex]

More can be learned about proportions at https://brainly.com/question/24372153

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