I have a logistic model function:
$$ y=\frac{424.92}{1+0.37027e^{0.000715x}}$$
This exponential model has an asymptote at $y=0$, and hence doesn't ever meet the $x$-axis. However, I need to discern when the quantity being measured ceases to exist (i.e. when it reaches zero). Is there some way I can calculate this anyway? Is there some cut-off point where I decide that the $y$-value becomes negligible?
The quantity is never $0$, but you can find the value of $x$ after which it becomes arbitrarily small. Say we want to know when we have $y<\varepsilon$ for some small positive number $\varepsilon$. Then we have $$\frac{424.92}{1+0.37027 e^{0.000715x}}<\varepsilon.$$ Taking reciprocals: $$\frac{1+0.37027 e^{0.000715x}}{424.92}>\varepsilon$$ and solving for $x$:$$\frac{424.92\varepsilon-1}{0.37027}<e^{0.000715x}$$ $$\log{\left(\frac{424.92\varepsilon-1}{0.37027}\right)}/0.000715<x.$$ So for any $x$ larger than this quantity, you will have $y<\varepsilon$. So, you can decide what value of $\varepsilon$ can be considered as "negligible" in your model and then find what value of $x$ makes your $y$ this small.