The growth rate of a population showing logistic growth is zero when

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

K is infinity

K is far greater than N

N equals K

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The logistic growth model takes into account the carrying capacity (K) of the environment, which is the maximum number of individuals that can be supported in a given area.
The logistic growth model can be expressed as $fraction numerator d N over denominator d t end fraction equals r N space open parentheses fraction numerator K minus N over denominator K end fraction close parentheses$ where,
$fraction numerator d N over denominator d t end fraction$ = growth rate (rate of change in population size over time)
r = intrinsic rate of natural increase
N = population density at time t
K = carrying capacity
When the population size (N) equals the carrying capacity (K), the logistic growth equation simplifies to $fraction numerator d N over denominator d t end fraction equals r N space open parentheses fraction numerator K minus N over denominator K end fraction close parentheses space equals space r N space open parentheses 1 minus N over K close parentheses equals r N space open parentheses 1 minus 1 close parentheses equals space r N open parentheses 0 close parentheses space equals space 0$ This means that the population is no longer growing because it has reached its maximum sustainable size in the given environment. At this point, the growth rate of the population is zero, and the population size remains stable.

Watch 3-min video & get full concept clarity