Chapter 2.1, Problem 17E

Pesticides that kill all insect species are not only bad for the environment, but they can also be inefficient at controlling pest species. Suppose a pest insect species in a particular field has population R(t)a time t,and suppose its primary predator is another insect species with population F(t)at time t. Suppose the populations of these species are accurately modeled by the system
$\begin{array}{l}\frac{dR}{dt}=2R-1.2RF\\ \frac{dF}{dt}=-F+0.9RF\end{array}$

studied in this section. Finally, suppose that at time t= 0 a pesticide is applied to the field that reduces both the pest and predator populations to very small hut nonzero numbers.
(a) Using Figures 2.3 and 2.5,predict what will happen as t increases to the population of the pest species.
(b) Write a short essay, in nontechnical language, warning of the possibility of the ‘paradoxical” effect that pesticide application can have on pest populations.