The population of a town increases at a rate proportional to its population. Its initial population is 1000. The correct initial value problem for the population, $P ( t )$ , as a function of time, t, is
A) $\frac { d P } { d t } = k P , P ( 0 ) = 1000$
B) $\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 100$
C) $\frac { d P } { d t } = k P , P ( 0 ) = 100$
D) $\frac { d P } { d t } = k P ( 1 - P ) , P ( 0 ) = 100$
E) $\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 1000$

Question

Quizplus · Accepted Answer

The rate of population increase is proportional to its current population, which is described by the differential equation $\frac{dP}{dt} = kP$, and the initial population is given as 1000, making $P(0) = 1000$ the correct initial condition.

The Population of a Town Increases at a Rate Proportional P(t)P ( t )P(t)

The Population of a Town Increases at a Rate Proportional $P ( t )$