- #1

HeLiXe

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## Homework Statement

The rhinoceros is now extremely rare. Suppose enough game preserve land is set aside so that there is sufficient room for many more rhinoceros territories than there are rhinoceroses. Consequently there will be no danger of overcrowding. However if the population is too small, the fertile adults will have difficulty finding each other when it is time to mate. Write a differential equation that models the rhinoceros population based on these assumptions. (Note that there is more than one reasonable model that fits these assumptions.)

## Homework Equations

## The Attempt at a Solution

Ok so if I were to model this--I would say that the rate of change in the rhinoceros population with respect to time is proportional to the size of the population times the parameter which would be the growth coefficient...and the growth coefficient would be affected if the population is small. There are no limiting resources or predators...

Independent variable = time (t)

Dependent variable = population of rhinoceroses (P)

Parameter = (k)

I've never used LaTex before -_-

so it would be basic unlimited population growth model to start with

dP/dt = kP

but I think there would need to be another parameter (g) the smallest possible population for which the adults can still meet. So if P < g then dP/dt < 0...and I'm not sure how to express that in the model .