When does the growth rate of a population following the logistic model...
-N/K), where N is the population size, t is time, r is the intrinsic growth rate, and K is the carrying capacity.
The growth rate of a population following the logistic model equals zero when dN/dt = 0.
Setting dN/dt = rN(1-N/K) equal to zero, we can solve for N:
rN(1-N/K) = 0
N(1-N/K) = 0
N = 0 or N = K
Therefore, the growth rate of the population will equal zero when the population size is either zero or at the carrying capacity. At zero population size, there is no growth, and at carrying capacity, the population size remains constant.
When does the growth rate of a population following the logistic model...
Logistic growth of a population size occurs when resources are limited. The formula we use to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate.
The logistic model is given as dN/dt = rN(1-N/K)
When the value of N/K is one, then,
dN/dt = rN(1-N/K)
dN/dt = rN(1-1)
dN/dt = rN(0)
dN/dt = 0 (zero)
So, the growth rate of population will be equal to zero.