The Verhulst-Pearl logistic growth model represents population growth with a limiting factor, \( K \), which is the carrying capacity of the environment.
- \( r \) represents the intrinsic rate of natural increase.
\[ \begin{array}{|c|c|} \hline \textbf{Symbol} & \textbf{Meaning} \\ \hline K & \text{Carrying Capacity (Maximum population size)} \\ r & \text{Intrinsic Rate of Natural Increase} \\ \hline \end{array} \]
- \( K \) is the maximum population size that the environment can sustain indefinitely, taking into account resource limitations.
Thus, the correct answer is (3) Carrying capacity.
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :