One can write a logistic function in the following form:
$y(t) = \frac{K}{\left(1 + Q \exp(-bt)\right)^{1/v}}$
where $v>0$ is considered a parameter, and $b$ is called the growth rate parameter. I am slightly confused as to the nature of this growth rate parameter, as this equation implies that it is a constant. But, when I read the phrase "growth rate", I read it as $dy/dt$, which is not just $b$. Can someone please explain the nature of $b$?
Further, say you had a bunch of y-values, say $(100,300,350,400,450,600,690,691,692)$. Could you estimate what $r$ was by looking at these values, assuming that $t=(1,2,3,4,5,6,7,8)$?
Thanks.
For ordinary exponential growth governed by $y(t) = c e^{rt}$ we call $r$ the growth rate even though $dy/dt = ry$ is not constant. In this case as in yours the growth rate is essentially a proportion. Its units are $1/\text{time}$.