Organisms and Populations Question 40
40. Asymptote in a logistic growth curve is obtained when :
[2017]
(a) $K=N$
(b) $K>N$
(c) $K<N$
(d) The value of ’ $r$ ’ approaches zero
Show Answer
Answer : a
Hints & Solutions
(a) In logistic growth curve, the curve has an upper a symptote known as carrying capacity $(K)$ is obtained when the maximum population size is at $\frac{d N}{d t}=0$. A population growing in a habitat with limited resources shows logistic growth curve.
For logistic growth,
$ \begin{aligned} & \frac{dN}{dt}=rN(\frac{K-N}{K}) \\ & \text{ If } K=N \text{ then } \frac{K-N}{K}=0 \end{aligned} $
$\therefore \quad \frac{dN}{dt}=0$.
The population reaches asymptote.
Carrying capacity is widely used as an indicator of environmental sustainability. It often serves as the basis for sustainable development policies that attempt to balance the needs of today against the resources that will be needed in the future.
