Question

When does the growth rate of a population following the logistic model equal zero? The logistic model is given as $\frac{DN}{dt}$ $=rN(1-\frac{N}{K})$

• A. When $\frac{N}{K}$ is exactly one
• B. When N nears the carrying capacity of the habitat
• C. When $\frac{N}{K}$ equals zero
• D. When death rate is greater than birth rate

Answer 1

The correct option is A When $\frac{N}{K}$ is exactly one

In logistic growth model population, equation is described is described as $\frac{DN}{dt}$ $=rN(1-\frac{N}{K})$
where, N = Population density at time t
r = Intrinsic rate of natural increase
K = carrying capacity
when, $\frac{N}{K}$ = 1
Now $\frac{K-N}{K}=0.$
So this will be $\frac{K}{K}-\frac{N}{K}$
1-1=0
Therefore dN/dt = 0