A desert preserve in the southwest is known for its populations of coyotes and road runners.The growth rate for each population can be modeled by this pair of differential equations: $\begin{array} { l }
\frac { d R } { d t } = 2 R - 0.2 R C \
\frac { d C } { d t } = - 1.4 C + 0.02 R C
\end{array}$ where C is the number of coyotes and R is the number of road runners.Find the equilibrium populations for this model.(Hint: These are the populations for which $\frac { d R } { d t } = \frac { d C } { d t } = 0$ ).
A)60 coyotes,15 road runners
B)10 coyotes,70 road runners
C)15 coyotes,60 road runners
D)70 coyotes,10 road runners

Question

A desert preserve in the southwest is known for its populations of coyotes and road runners.The growth rate for each population can be modeled by this pair of differential equations: $\begin{array} { l } 
\frac { d R } { d t } = 2 R - 0.2 R C \
\frac { d C } { d t } = - 1.4 C + 0.02 R C
\end{array}$ where C is the number of coyotes and R is the number of road runners.Find the equilibrium populations for this model.(Hint: These are the populations for which $\frac { d R } { d t } = \frac { d C } { d t } = 0$ ).
A)60 coyotes,15 road runners
B)10 coyotes,70 road runners
C)15 coyotes,60 road runners
D)70 coyotes,10 road runners

Quizplus · Accepted Answer

The Answer is B

A Desert Preserve in the Southwest Is Known for Its dRdt=2R−0.2RCdCdt=−1.4C+0.02RC\begin{array} { l } \frac { d R } { d t } = 2 R - 0.2 R C \\\frac { d C } { d t } = - 1.4 C + 0.02 R C\end{array}dtdR​=2R−0.2RCdtdC​=−1.4C+0.02RC​

A Desert Preserve in the Southwest Is Known for Its $\begin{array} { l } \frac { d R } { d t } = 2 R - 0.2 R C \\\frac { d C } { d t } = - 1.4 C + 0.02 R C\end{array}$