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  4. The population growth is generally described by the following equation: (dN/dt)=rN((K-N/K)) What does 'r' represent in the given equation ?

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Q. The population growth is generally described by the following equation :
$\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$
What does '$r$' represent in the given equation ?

KEAMKEAM 2014Organisms and Populations

Solution:

A population growing in a habitat with limited resources shows initially a lag phase, followed by phases of increase and decrease and finally the population density reaches the carrying capacity. A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst- Pearl Logistic Growth as explained by the following equation :
$dN / dt = rN \left( \frac{K - N }{K} \right)$
Where N = Population density at a time t;
r = Intrinsic rate of natural increase and;
K = Carrying capacity.