The logistic curve is the graph of the function $$f(x) = \frac{a}{1+be^{-rx}}$$ where $a$, $b$, and $r$ are suitable parameters.
This function may describe, for example, the initial rapid growth of a population, followed by a slowdown of the growth as resources become sparse. Since $e^{-rx}$ tends to zero as $x$ tends to infinity $f(x)$ approaches $a$ as $x$ tends to infinity, and at $x=0$ the initial population equals $$f(0) = \frac{a}{1+b}.$$ The rate $r$ is the usual growth rate that would prevail indefinitely in the presence of unlimited resources.

Suppose $a=1100$, $b = 60$, and $r=0.01$. Then the initial population is and as time goes on the population approaches but never quite reaches .