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

AP Calculus ABeasymcq1 pt

Which of the following functions satisfies $\dfrac{dy}{dx} = -3y$ and $y(0) = 4$ ?

A.

y = 4e^{-3x}

B.

y = e^{-3x} + 3

C.

y = 4e^{3x}

D.

y = 4e^{-x}

Explanation

Core Concept

At $x=0$ the function equals $4$ , and $y' = -12e^{-3x} = -3(4e^{-3x}) = -3y$ , so both conditions hold.

Correct Answer

A $y = 4e^{-3x}$

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