The rhino is now extremely rare! Suppose, if there are too few rhinos (less than

Question

The rhino is now extremely rare!

Suppose, if there are too few rhinos (less than M), the poplulation will die off because not enough fertile adults find mates.

On the other hand, suppose the environment can only handle so many fertile rhinos. Thus, there is a population N, which when exceeded, will cause the population to head back down toward this carrying capacity N.

Also, assume if the rhino population P is such that M < P < N, then P is increasing.

Write a differential equation that models the rhino population, based on these assumptions. Hint: Take terms from two different models, and this should go will for you!

Explanation / Answer

Suppose the population at time t is denoted as P(t)

and let k be the growth factor

dP/dt must be negative if it decreases the threshold extinction value

so, dP/dt = kP - M/P

where k is the growth factor

------------

if it is to not cross the holding capacity

then,

dP/dt = kP - N

again if it is positive we will knw it has exceeded the maximum threshold

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