Question

Asymptote in a logistic growth curve is obtained when

Answer 1

Logistic growth curve

Logistic growth curve is shown by the population growing in an environment lacking apparently unlimited resources.

The growth can be represented by a sigmoid curve. It is denoted by the following equation:

$\frac{dN}{dt}=rN\frac{(K-N)}{K}$

$=rN(1-\frac{N}{K})$

Logistic growth curve

Where,
$N=$ Population density
$r=$ Intrinsic rate of natural increase
$K=$ Carrying capacity

Trends of Logistic growth curve
A population inhabiting a habitat with limited resources shows logistic growth curve with the following phases:

• A lag phase during the initial stage.
• After the initial stage, it shows accelerated growth as the population increases and utilises the resources.
• The resources get utilised at the later stages and thus the growth deaccelerates. Finally, it turns into an asymptote when the population density becomes equivalent to the carrying capacity of the environment.
• So, in the case of an asymptote, $K=N.$

Final answer
(a) $K=N$