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

The population of a town increases at a rate proportional to its population. Its initial population is 5000. The correct initial value problem for the population, $P ( t )$ , as a function of time, t, is

A) $\frac { d P } { d t } = k P , P ( 0 ) = 5000$
B) $\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 500$
C) $\frac { d P } { d t } = k P , P ( 0 ) = 500$
D) $\frac { d P } { d t } = k P ( 1 - P ) , P ( 0 ) = 5000$
E) $\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 5000$