A slope field for is shown to a student

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

Problem

A slope field for

\dfrac{dy}{dx}=y(2-y)

is shown to a student. Four descriptions of the solution curve that passes through

(0,3)

are offered. Which description is most consistent with the field? (a) The curve decreases and approaches

y=0

x

increases. (b) The curve increases without bound as

x

increases. (c) The curve decreases and approaches

y=2

x

increases. (d) The curve decreases without bound, tending toward

-\infty

x

increases.