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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Definitions:

Capitalized

The process of recording an expenditure as an asset, rather than an expense, allowing it to be expensed over time through depreciation or amortization.

Inventory

The total value of a company's holdings of goods and materials that are to be sold, are in process of being produced, or are used in producing goods.

Period Costs

Costs that are not directly tied to the production process and are expensed in the period they are incurred, such as selling and administrative expenses.

General Costs

Broadly, expenses that are not directly tied to a specific product or service, often including overhead costs.