NEET2026BiologyChapterActual
The given figure illustrates the growth curve of a population in a habitat with limited resources. If N is the population density at time t , r is the intrinsic rate of natural increase, and K is the carrying capacity, which of the following statements correctly describes the state of the population at point 'P'? [refer to the image]
Options
- AThe value of ( K-N K ) approaches zero, causing the population growth rate ( dN dt ) to approach zero.
- BThe value of ( K-N K ) approaches one, allowing the population to grow at a maximum rate of rN .
- CThe population is in the acceleration phase, and the value of ( K-N K ) is negative.
- DThe population density N has exceeded the carrying capacity K , resulting in a negative growth rate.
Correct answer
A. The value of ( K-N K ) approaches zero, causing the population growth rate ( dN dt ) to approach zero.
Step-by-step solution
The given figure represents a logistic growth curve, which is described by the Verhulst-Pearl Logistic Growth equation: dN dt = rN ( K-N K ) where: N = Population density at time t r = Intrinsic rate of natural increase K = Carrying capacity At point 'P' on the curve, the population has reached its carrying capacity, meaning N K . Substituting N = K into the term ( K-N K ) , we get: ( K-K K ) = 0 As the value of ( K-N K ) approaches zero, the population growth rate ( dN dt ) also approaches zero. This indicates tha