Mathematics

Problem

Three separate slope fields correspond to the differential equation

\displaystyle \frac{dy}{dx}=a y

, where

a

is a positive constant. At the point

(0,1)

the approximate slopes of the line elements are measured to be

0.5

in Field I,

1.0

in Field II, and

2.0

in Field III. Which relationship among the parameter values

a_I,\,a_{II},\,a_{III}

is most consistent with these observations? a)

a_I=a_{II}=a_{III}

a_I>a_{II}>a_{III}

a_I<a_{II}<a_{III}

a_I<a_{III}<a_{II}