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) :

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) : (A) When N nears the carrying capacity of the habitat (B) When N/K equals zero. (C) When death rate is greater than birth rate (D) When N/K is exactly one.

Tardigrade Admin · Accepted Answer

In logistic growth model population growth equation is described as

\frac{d N}{d t} = r N (\frac{K - N}{K})

where,
N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
When, N/K = 1 then

\frac{K - N}{K} = 0

∴ \frac{d N}{d t} = 0

Q. 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) :

When N nears the carrying capacity of the habitat

When N/K equals zero.

When death rate is greater than birth rate

When N/K is exactly one.

In logistic growth model population growth equation is described as dtdN​=rN(KK−N​) where, N = Population density at time t r = Intrinsic rate of natural increase K = Carrying capacity When, N/K = 1 then KK−N​=0 ∴dtdN​=0

In logistic growth model population growth equation is described as
$\frac{d N}{d t} = r N (\frac{K - N}{K})$
where,
N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
When, N/K = 1 then
$\frac{K - N}{K} = 0$
$∴ \frac{d N}{d t} = 0$