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

AP Calculus ABeasymcq1 pt

A population $P(t)$ grows at a rate proportional to its size. Which differential equation describes this growth?

A.

\dfrac{dP}{dt} = kP

B.

\dfrac{dP}{dt} = kt

C.

\dfrac{dP}{dt} = \dfrac{k}{P}

D.

\dfrac{dP}{dt} = kP^2

Explanation

Core Concept

Proportional growth means the rate $\dfrac{dP}{dt}$ equals a constant multiple of the current population $P$ .

Correct Answer

A $\dfrac{dP}{dt} = kP$

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