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.
