Question

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

Answer 1

Calculations

When $\frac{N}{K}=1$

$\frac{dN}{dt}=rN(1-\frac{N}{K})$

$\frac{dN}{dt}=rN(1-1)$

$\frac{dN}{dt}=rN\times 0$

$\frac{dN}{dt}=0$

Hence, the growth rate of a population becomes zero when $\frac{N}{K}$ gets exactly equal to one.

In other words, population density at time ${}^{\prime }{t}^{\prime }$ is exactly equal to the carrying capacity of the habitat.

Final answer
(c) When $\frac{N}{K}$ is exactly one