calc help w/ predator-prey systems?

Question

For each predator-prey system, determine which of the variables, x or y, represents the prey population and which represents the predator population. Is the growth of the prey restricted just by the predators or by other factors as well? Do the predators feed only on the prey or they have additional food sources? Explain.

a) dx/dt = -0.05x + 0.0001xy
dy/dt = 0.1y - 0.005xy

b) dx/dt = 0.2x - 0.0002x^2 - 0.006xy
dy/dt = -0.015y + 0.00008xy

show work/steps plz..thanks!

Answer 1

There is no calculus involved here, so what is your real problem?

Looking at problem a:
in the formula for dx/dt, what is the sign of the term in y? So for a fixed x, if y is higher, will dx/dt be higher or lower? (recall that dx/dt is how fast x changes with time (and in which direction))

and in the formula for dy/dt, ditto for x.

In the real world, the more rabbits there are, the faster the population of foxes will grow; but the more foxes there are, the slower the rabbit population will grow (and it may even shrink)

The other questions similarly relate biology with the various coefficients of the formula. For example, if dx/dt has an x term with a large positive coefficient, then the more x the merrier - competition is not a critical factor (at least up to a point - perhaps the carrying capacity of the land?). If the coefficient is negative, then competition is a factor even when the numbers are small.

Answer 2

while God created the worldwide thousands and thousands of years in the past in the 1st Earth Age, existence wasn't like that. It grow to be merely while devil presented sin into the worldwide did suffering come alongside with it. it is the 2d Earth Age. in the 0.33 Earth Age, all would be lower back to perfection because it grow to be earlier. there have been no predators (or if there have been, they have been herbivores), no parasites, no ailment, discomfort or suffering of any form. devil rebelled in the 1st age, so the 2d age grow to be created to furnish guy a decision between following God or no longer. it somewhat is the place suffering comes from. i'm no longer asserting animals are evil; they're neither inherently solid nor evil, yet all suffering is an extension of devil.