In a pair of interacting populations

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

In a pair of interacting populations, the rates satisfy

\frac{dX}{dt}=k\,Y, \qquad \frac{dY}{dt}=k\,X,

where

k

is a constant. At one instant the counts are

X=600

and

Y=400

, and

X

is observed to be increasing at

80

individuals per hour. What is the value of

k

? (a)

0.13\,\text{h}^{-1}

(b)

0.20\,\text{h}^{-1}

(c)

-0.20\,\text{h}^{-1}

(d)

0.08\,\text{h}^{-1}