## How long will it take to get 10,000 subscribers...?

The question above is a variation of a question that has come up multiple times in past meetings at a company I'm working with. It's a variation of the ROI discussion. And, it's rearing its head again as we prepare to roll out a subscription-based online training/social network in a couple of months.

And, oh, I should say I'm not writing about it here so I can give a definitive answer. Far from it. **I'm hoping one/some of you might be able to help with models you've encountered.**

But, as is my nature (at least, I like to think it is) I'm not coming to the table with you empty-handed.

(Photo courtesy: mseery on Flickr, creative commons.)

## One of many

While I'm familiar with "laws" attributable to Metcalfe, Reed, Sarnoff and Odlyzko-Briscoe-Tilly (which I like better than the others, btw... I'll save that for a future post), those are really more about interpreting "value," however * that's* to be perceived.

The **"How long...?"** question is one related to growth rates, I know. And, since I don't have anything empirical (yet?) I've gone in search of naturally-occurring growth phenomenon as one approach to answer the question. I mean, so obsessed am I that I've gone into the gutters--the garbage even--to find answers. You know, the stuff of bacteria...maggots, germs...like that... I'm talking about "*e*^{x}", the symbol for an exponentially occurring growth rate.

Actually, in this case, since it's a time-related question I'm obsessed with (who isn't obsessed with time?), I guess I'd be coming to the table with ** e**'s opposite twin, the "natural logarithm" (symbol: LN(n)... which, they taught me in high school to say, "ell-en of n", where "n" is a reference to a period of time for something associated with a 100% compounded growth rate. That is, let's say I start with 500 units of something. One "n" would then be the period of time it takes to grow another 500 units.

Now, please understand, I may be anal retantive ritentiv retentive, but I'm no "quant". Far from it. I barely got a C in high school Algebra. But, I'm much better now. I actually picked up the ability to read and research along the way. If you want to dig deeper, here's a pretty good explanation of Demystifying the Natural Logarithm (ln) by Kalid Azad.

## The high level

So, one approach in forecasting the time required to grow to, say, 10,000 subscribers is to begin with two questions:

**1. How many do you have now**? (Or, a variation: How many did you have...[last quarter, last year, two years ago, etc.]?) Let's say the answer to this is a current subscriber base of **500 users**.

**2. How long did it take you to grow to your current subscriber base?** (Or, a variation: How long did it take you to grow to the subscriber base you had... [last quarter, last year, two years ago, etc.]?) For grins and giggles, let's say it took **5 months** to get those 500 subscribers.

Then you say, okay, whatever the answer is to #1 above, that's one "**n**" (1n). And, whatever the answer was to #2? That's, one **period**. (LN(n)).

Then, the approach would be to use the LN function on any scientific calculator to calculate the natural log (resulting periods) of the number of "n"s your goal represents. In this case, 10,000.

Got all that? Hmm... let's work an example.

## Example

In my setup above, I said we currently have 500 users. (500 = 1n).

And, I said it took 5 months to get there. (5 months = 1 period.)

The question is, how long to get 10,000 users? (n = 10,000/500 = 20).

To get the number of periods that represents, enter "20" in any scientific calculator and then push the "LN" button. (Or, using the simple table below, find 20 under the "n" column, then read the corresponding LN (periods).

Result: **3**.

**Answer: That implies, it would take about three 5-month periods (15 months total) to grow to 10,000 users.**

Okay, just remember, this is a model, right? As such, we have to remember that models basically say, "Within certain caveats, I'm reasonably correct. Outside of those caveats, I don't make sense."

A key caveat in this case: we're assuming that the underlying growth rate of the thing being measured follows an exponential growth scenario... essentially, it grows continuously at a rate of 100% compounded every period. That is, 1...2...4...8...16, like that.

Allright, your turn. If you've come across other models, please post 'em in the comments below. And, if there are any corrections for me from you math majors, I'm open to 'em. Be gentle. ;)

If you liked this, or any of the articles on this site, please subscribe!

Are you a fellow "Tweep"? Follow me on Twitter (@melaclaro).

Or, connect with me on LinkedIn: LinkedIn.com/in/melaclaro.

Got friends? Forward this post or save it to any of the bookmarking sites below.