Chapter 6.6, Problem 31E

(a)

To determine

The model that the prey population would follow when there are no predators where;

$\begin{array}{l}\frac{dx}{dt}=ax\left(1-\frac{x}{L}\right)-bxy\\ \frac{dy}{dt}=-my+nxy\end{array}$

(b)

To determine

To calculate: The revised model for the provided parameters and its critical numbers where:

$\begin{array}{l}\frac{dx}{dt}=ax\left(1-\frac{x}{L}\right)-bxy\\ \frac{dy}{dt}=-my+nxy\end{array}$

(c)

To determine

To graph: The functions for x and y versus time t when t is between 0 and 72 where:

$\begin{array}{l}\frac{dx}{dt}=0.4x\left(1-\frac{x}{100}\right)-0.001xy\\ \frac{dy}{dt}=-0.3y+0.005xy\end{array}$

(d)

To determine

To graph: The slope field for the provided predator prey model when x is between 0 and 100 and y is between 0 and 80 where:

$\begin{array}{l}\frac{dx}{dt}=0.4x\left(1-\frac{x}{100}\right)-0.001xy\\ \frac{dy}{dt}=-0.3y+0.005xy\end{array}$

(e)

To determine

To graph: The solution for the provided predator prey model in the slope field when x is between 0 and 100 and y is between 0 and 80 where:

$\begin{array}{l}\frac{dx}{dt}=0.4x\left(1-\frac{x}{100}\right)-0.001xy\\ \frac{dy}{dt}=-0.3y+0.005xy\end{array}$