Consider the differential equation

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

Problem

\dfrac{dy}{dt}=y(1-y)

. A solution curve starts at the point

(0,0.40)

. Which of the following best describes the long-term behavior of the solution as

t\to\infty

? (a) It decreases and approaches

y=0

. (b) It increases without bound. (c) It increases and approaches

y=1

. (d) It increases and approaches

y=0.5