Consider the differential equation

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

Problem

\displaystyle \frac{dy}{dx}=y\left(1-\frac{y}{K}\right)

, where

K>0

is a constant. In its slope field, horizontal line elements are observed along the line

y=4

. Which value of

K

is most consistent with this observation? (a)

K=8

(b)

K=4

(c)

K=\dfrac{16}{3}

(d)

K=16