Let X Be the Number of Reptiles, Y Be the Number

question 24

Short Answer

Let x be the number of reptiles, y be the number of mammals, and z be the number of plants on the island of Komodo, all measured in thousands (e.g., x = 50 means 50,000 reptiles).The following differential equations give the rates of growth of reptiles, mammals, and plants on the island: $\begin{array}{l}\frac{d x}{d t}=-0.2 x-0.04 x y+0.0008 x z \\\frac{d y}{d t}=-0.1 y+0.01 x y \\\frac{d z}{d t}=2 z-0.002 z^{2}-0.1 x z\end{array}$ Say that initially there are 100,000 plants on Komodo, and there are no reptiles or mammals.At what plant population would the number of plants be increasing the fastest?

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