I need to come up with the (Excel) formula for a 'hockey stick' graph. Although the numbers do not really matter, here's what I need to show: time line 24 months, saturation value 12,000,000.
I hope this makes (some) sense.
Let's say you start a new service and at the beginning you double your subscriber base every week then every month then every quarter and you reach saturation at about 2,000,000 subscribers within 24 months.
How would an (Excel) formula for that scenario look like?
You need the Verhulst equation, which has solution:
$\displaystyle
S(t)=\frac{K S(0)\ e^{rt}}{K+S(0)\ (e^{rt}-1)}
$
Where $\displaystyle S(0)$ is the initial number of subscribers, and $\displaystyle r$ is the initial growth constant (in your case 2/wk, so if you measure time $\displaystyle t$ in weeks has a value of 2), and $\displaystyle K$ is your saturation level.
RonL