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

question 1

Multiple Choice

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) \(\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 1000\)

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