A certain population increases at a rate proportional to the square root of the population. If the population goes from 2500 to 3600 in five years, what is the population at the end of t years

Step-by-step explanation:

A certain population increases at a rate proportional to the square root of the population.

This means that the population can be described by the following differential equation:

In which r is the growth rate.

Solving by separation of variables, we have that:

Integrating both sides:

In which K is a random constant

Finding the squares of both sides:

Finding the value of K

The initial population is of 2500. That is, when . So

So

Finding the value of r

Population of 3600 in 5 years(when t = 5). So

Taking the square root of both sides

So, the equation for the population at the end of t years is given by:

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step-by-step explanation:

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