The system of differential equations $$\frac{1}{x}\,\frac{dx}{dt} = y - 1 - 0.02 x, \qquad \frac{1}{y}\,\frac{dy}{dt} = 1 - x - 0.02 y$$ model the interaction of two populations $x$ and $y$.

(a) What kind of interaction do these equations describe?
? symbiosis competition predator-prey
(Symbiosis takes place when the interaction of two species benefits both. An example is the pollination of plants by insects.)

(b) Now suppose that we start with the initial populations $(x(0), y(0)) = (1,3.5)$. What happens to the populations in the long run?
The population $x$ ? goes to zero goes to one goes to infinity oscillates
The population $y$ ? goes to zero goes to one goes to infinity oscillates
(To answer this question you will want to use a calculator or computer to draw slope fields.)