Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 9.6, Problem 1PT
To determine

Whether the statement “Predator-prey population models are the solutions to two differential equations” is true or false.

Expert Solution & Answer
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Answer to Problem 1PT

The statement “Predator-prey population models are the solutions to two differential equations” is true_.

Explanation of Solution

Definition used:

Predator-prey population equation:

The populations R(t) and W(t) are modeled by a pair of predator-prey equation, dRdt=kRaRW and dWdt=rW+bRW, where k ,r ,a and b are positive constants.

Description:

Here, R(t) is the number of prey at time t and W(t) is the number of predators at time t.

Thus, R(t) and W(t) are two equations and they are differentiable.

Predator-prey population models are used to link the two linear differential equations by using the definition mentioned above.

Note that, the values of R and W are found by solving the equations dRdt=0anddWdt=0.

Therefore, the statement “Predator-prey population models are the solutions to two differential equations” is true_.

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