Consider a population governed by with and

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Consider a population governed by

\dfrac{dy}{dt}=r y\,(K-y)

with

r>0

and

K>0

. Describe whether the population is increasing or decreasing when

0<y<K

, and give a brief reason based on the sign of

\dfrac{dy}{dt}