NEET Solved Paper 2016 Question 65
Question: When does the growth rate of a population following the logistic model equal zero? The logistic model is given as $ dN/dt=rN(1-N/K) $ :
Options:
A) When $ N/K $ is exactly one
B) When $ N $ nears the carrying capacity of the habitat
C) When $ N/K $ equals zero
D) When death rate is greater than birth rate
Show Answer
Answer:
Correct Answer: A
Solution:
- The logistic model for population growth is given by the equation:
[ \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right) ]
where:
- ( \frac{dN}{dt} ) is the growth rate of the population,
- ( r ) is the intrinsic growth rate,
- ( N ) is the population size,
- ( K ) is the carrying capacity of the habitat.
To determine when the growth rate equals zero, we set the equation to zero:
[ rN \left(1 - \frac{N}{K}\right) = 0 ]
This equation will be zero when either:
- ( N = 0 ), or
- ( 1 - \frac{N}{K} = 0 )
Solving the second condition:
[ 1 - \frac{N}{K} = 0 ] [ \frac{N}{K} = 1 ] [ N = K ]
So, the growth rate of the population equals zero when ( N = K ), which means the population size ( N ) is equal to the carrying capacity ( K ).
Now, let’s match this with the given options:
A) When ( N/K ) is exactly one B) When ( N ) nears the carrying capacity of the habitat C) When ( N/K ) equals zero D) When death rate is greater than birth rate
BETA
