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Problem 4 Easy Difficulty

Lynx eat snowshoe hares and snowshoe hares eat woody plants like willows. Suppose that, in the absence of hares, the willow population will grow exponentially and the lynx population will decay exponentially. In the absence of lynx and willow, the hare population will decay exponentially. If $ L(t), H(t), $ and $ W(t) $ represent the populations of these three species at time $ t, $ write a system of differential equations as a model for their dynamics. If the constants in your equation are all positive, explain why you have used plus or minus signs.

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Video Transcript

it was for So we know that means we eat snowshoe hares and a social hairs eat, we lose or care. So there to situations The first one says, um, that hairs are not president. So this is true. Then we want to see how the links and wills well, how the wings be here. So you could write down the director derivative off the wills respected Time is going to equal to que times w minus k times. So this is true because the here the Williams will grow exponentially. That's why it's a positive. It w and then the limbs will dig caves full. Actually, that's really we have the negative K times. So Ah, the second situation is that the links and there would low are not present. This is true. We want to see how the, um Harris change with time so we could write down derivative off h respected time. And then h is, um here's so what will happen to them? Well, we know that the hair publisher will be care exponentially so we could write need okay times each. And that is a