For the differential equation with initial condition

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

Problem

For the differential equation

\dfrac{dy}{dx}=y

with initial condition

y(0)=1

, a student follows the slope field by drawing successive tangent segments of length

0.2

in the

x

-direction. Starting at

(0,1)

and continuing in the positive

x

-direction, which value is the most reasonable estimate of

y

when

x=0.4

? (a)

1.64

(b)

1.44

(c)

1.49

(d)

1.40