Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABhardmcq1 pt

The slope field for $\dfrac{dy}{dx} = y$ is shown. If a solution curve passes through the point $(0,-2)$ , what happens to $y$ as $x$ increases?

A.It decreases toward

0

without ever reaching it.

B.It increases without bound.

C.It decreases without bound.

D.It increases toward

0

without ever reaching it.

Explanation

Core Concept

With $y=-2$ , the slope is $-2<0$ , so $y$ decreases further; the solution $y=-2e^x$ goes to $-\infty$ as $x$ increases.

Correct Answer

CIt decreases without bound.

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