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  • Need clarity, kindly explain! Population of a country increases at the rate proportional to its instantaneous value,then the differential equation will be

Population of a country increases at the rate proportional to its instantaneous value,then the differential equation  will be

  • Option 1)

    \frac{dN}{dt}=KN

  • Option 2)

    \frac{dN}{dt}=K\sqrt N

  • Option 3)

    \frac{dN}{dt}=KN^{2}

  • Option 4)

    \frac{dN}{dt}=KN^{3}

 

Answers (1)

best_answer

As we have learned

Growth and Decay Problems -

\frac{dN}{dt}= KN

- wherein

K is the Constant of proportionality

 

 Let N be the number of population at time 't' 

\therefore \frac{dN}{dx}\propto N\Rightarrow \frac{dN}{dt}= KN

 


Option 1)

\frac{dN}{dt}=KN

Option 2)

\frac{dN}{dt}=K\sqrt N

Option 3)

\frac{dN}{dt}=KN^{2}

Option 4)

\frac{dN}{dt}=KN^{3}

Posted by

prateek

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