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

AP Calculus ABmediummcq1 pt

A slope field for the differential equation $\dfrac{dy}{dx} = 0.5y$ is shown. Which family of curves do the solution curves resemble?

A.

y = Ce^{0.5x}

B.

y = 0.5x + C

C.

y = Ce^{-0.5x}

D.

y = 0.5x^2 + C

Explanation

Core Concept

Solving $\dfrac{dy}{dx} = 0.5y$ by separating variables gives $y = Ce^{0.5x}$ , so the solution curves are exponentials.

Correct Answer

A $y = Ce^{0.5x}$

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