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: $\begin{array}{l}
\frac{d x}{d t}=-0.2 x-0.04 x y+0.0008 x z \
\frac{d y}{d t}=-0.1 y+0.01 x y \
\frac{d z}{d t}=2 z-0.002 z^{2}-0.1 x z
\end{array}$ What would happen to the plants if the other two were not present?
A)They would experience logistic growth.
B)They would experience exponential decay.
C)They would remain constant.

Question

Quizplus · Accepted Answer

If the other two species (reptiles and mammals) were not present, the differential equation for plants becomes $\frac{d z}{d t}=2 z-0.002 z^{2}$, which is a logistic growth model, indicating that the plants would experience logistic growth.

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