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When does the growth rate of a population following the logistic modal equals zero? The logistic model is given as $\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$
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.
Explanation
Growth stops exactly when N = K.
Detailed Solution
$\frac{dN}{dt} = rN\left(\frac{K - N}{K}\right)$, where N = population density, r = intrinsic rate of natural increase, K = carrying capacity
When $\frac{N}{K} = 1$, $\frac{K - N}{K} = 0$, therefore $\frac{dN}{dt} = 0$.
When $\frac{N}{K} = 1$, $\frac{K - N}{K} = 0$, therefore $\frac{dN}{dt} = 0$.