Question

Asymptote in a logistic growth curve is obtained when

• A. The value of 'r' approaches zero
• B. K = N
• C. K > N
• D. K < N

Answer 1

The Correct Option is B

 The logistic growth model is used to describe the growth of a population limited by resources over time. It is mathematically expressed by the equation:

\(N(t) = \frac{K}{1 + \left(\frac{K - N_0}{N_0}\right) e^{-rt}}\)

where:

• \(N(t)\) is the population size at time \(t\).
• \(K\) is the carrying capacity of the environment.
• \(N_0\) is the initial population size.
• \(r\) is the intrinsic growth rate.
• \(e\) is the base of natural logarithms.

An asymptote is reached in the logistic growth curve when the population size \(N\) approaches the carrying capacity \(K\). This is because resources become limited and inhibit further population growth.

Let's examine each option:

• The value of 'r' approaches zero: A decrease in the intrinsic growth rate \(r\) does not directly result in an asymptotic behavior. It only slows the rate at which the population reaches carrying capacity.
• K = N: When the population size \(N\) equals the carrying capacity \(K\), the population size stabilizes, effectively forming an asymptote on the growth curve.
• K > N: In this scenario, the population is still growing towards carrying capacity, not forming an asymptote yet.
• K < N: If the population exceeds the carrying capacity, it will descend towards \(K\) due to resource limitations, not an asymptote state initially.

The correct answer is that an asymptote in a logistic growth curve is obtained when K = N.