The rate at which a population changes is directly proportional to the current population

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The rate at which a population

P(t)

changes is directly proportional to the current population. Which differential equation best expresses this relationship, where

k

is an unknown constant? (a)

\dfrac{dP}{dt}=k

(b)

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

(c)

\dfrac{dP}{dt}=kP

(d)

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