The differential equation has a slope field whose arrows become horizontal along the line

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The differential equation

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

has a slope field whose arrows become horizontal along the line

y=1

. Determine

\displaystyle \lim_{x\to\infty} y(x)

for the solution that satisfies

y(0)=0.8

, and give a brief reason based on the slope field.