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**preview**shows half of the first page. to view the full**1 pages of the document.**9.6 Differential Equations

Predator & Prey Systems

Question #1 (Easy): Understanding the Predator-Prey System

Strategy

Differential equations can be used to represent the prey and predator population rate of change system.

Given variables x and y, and the differential equations provided with terms that contribute to the

growth and decline in the rate of population growth, the predator and prey system can be analyzed.

Sample Question

For the predator-prey system, determine which variables of x and y represents the prey and predator

population. Is the growth of the prey restricted only by the predators or by other factors as well? Do the

predators feed only on the prey or on other food sources as well? Explain.

Solution

Notice that when ,

meaning it is declining in the absence of variable . The predators

feed on predator, therefore represents the predator population. Then the other variable represents

prey population. The growth of prey population is restricted by which only involves variable

and , thus it is restricted only by the predators and no other external factors. Likewise, the predator

population increases by the term which only involves variables and , thus there is no other

food source besides the prey.

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