#### Answer

(a) $\frac{dC}{dt} = 0$
$\frac{dW}{dt} = 0$
(b) $C=0$
(c) The population pairs that lead to stable populations are $(0,0)$ and $(500,50)$
Therefore, it is possible for the two populations to live in balance if there are 500 caribou and 50 wolves.

#### Work Step by Step

(a) If the populations are stable, then the populations are not changing. This means that the rate of change of the population is 0.
$\frac{dC}{dt} = 0$
$\frac{dW}{dt} = 0$
(b) The statement "The caribou go extinct" means that the caribou population is 0.
We would represent this mathematically as $~~~C=0$
(c) $\frac{dC}{dt} = 0$
$aC-bCW = 0$
$(0.05)C-(0.001)CW = 0$
$C(0.05-0.001~W) = 0$
$C=0~~$ or $~~W = 50$
$\frac{dW}{dt} = 0$
$-cW+dCW = 0$
$-(0.05)W+(0.0001)CW = 0$
$W~(-0.05+0.0001~C) = 0$
$W=0~~$ or $~~C = 500$
The population pairs that lead to stable populations are $(0,0)$ and $(500,50)$
Therefore, it is possible for the two populations to live in balance if there are 500 caribou and 50 wolves.