The differential equation models population growth
MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Applications and Interpretation · Calculus · Calculus
Problem
The differential equation dxdy=ry(1−Ky) models population growth, where r and K are positive parameters. When r is fixed, how does increasing the parameter K qualitatively affect the horizontal equilibrium lines in the associated slope field?
(a) Neither equilibrium line moves; the entire slope field simply becomes steeper.
(b) Both the upper and lower equilibrium lines move upward by the same amount.
(c) The upper equilibrium line moves upward, while the lower equilibrium line remains at y=0.
(d) The upper equilibrium line moves downward, while the lower equilibrium line remains at y=0.