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.

Answer to Problem 1PT

The statement “Predator-prey population models are the solutions to two differential equations” is $\underset{\_}{\text{true}}$.

Explanation of Solution

Definition used:

Predator-prey population equation:

The populations $R\left(t\right)$ and $W\left(t\right)$ are modeled by a pair of predator-prey equation, $\frac{dR}{dt}=kR-aRW$ and $\frac{dW}{dt}=-rW+bRW$, where k ,r ,a and b are positive constants.

Description:

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

Thus, $R\left(t\right)$ and $W\left(t\right)$ 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 $\frac{dR}{dt}=0\text{and}\frac{dW}{dt}=0$.

Therefore, the statement “Predator-prey population models are the solutions to two differential equations” is $\underset{\_}{\text{true}}$.