math is easy

keep mumbling "math is easy" to yourself over and over and eventually you will believe it.

If I were to walk up to you and say "I started with 1 customer and after 4 iterations, I ended up with 81."
You might say "I don't get it.  It doesn't make any sense to me.  How am I supposed to understand how you got there?"

Okay, that response is completely reasonable.

So instead, let's say I start with 1 person.  And that one person brings in 10 people.  Do you understand that? - yes.
And then of those 10 people, 3 people come back to use my product.  So now I have 1 person that led to 3.  Do you understand that? - yes.

And then of those 3 people, each of them brings in 10 new people AGAIN.  Do you understand that? - yes.
And so that gets me 30 (3 x 10) new people.  Does that make sense?  -yes.
And then from those 30 people, 3 out of every 10 will return.  That means 9 (3 x 3) people will return.
Does that make sense? - yes.  
After building from the previous run, that's how I went from 1 to 9.

Now those 9 returning patrons will each bring in 10 new people.  
9 x 10 = 90 new people.  Does that make sense? - yes.
Again, of those 90 people, 3 out of every 10 will come back to use my product.  So 3 x 9 = 27 people.  
Does that make sense? - yes.  
Again, building from the previous run, that's how I went from 1 to 27.

You probably get the pattern now, and so for the final iteration, those 27 people bring in 10 new people each gets me the formula of 27 x 10, which = 270.  Does that make sense? - yes.
And finally 3 out of every 10 (3/10 = 30%) of the 270 gets me 81 (3 x 27 = 81, or in other words 30% of 270 = 81) returning customers.  
I hate to sound like an ass, but this is maybe 2nd grade math.

And so now when I say "I started with 1 customer and after 4 iterations, I ended up with 81."
Does that make sense?" :)

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p.s. for those of you who just want the numbers and don't care for all the unnecessary words:
1 x 10 = 10
if 30% return, then = 3.
3 x 10 = 30
if 30% return, then = 9.
9 x 10 = 90
if 30% return, then = 27.
27 x 10 = 270
if 30% return, then = 81.
Therefore I started with 1, and after 4 iterations, I ended up with 81.