Difficult Exponential Growth Problem

[Bravoranger]

Hi, this is my first time using this forum so I apologize if this question doesn't fall into the appropriate category. My question is basically exponential growth, but with a few twists, hang onto your hats and I try to explain this. (If you want to know what the heck this is for just skip to the end)
I have a unit, which we'll call (x) for now. So unit (x) starts out as 1 unit, but every month (x) creates another 100 (x). And 10% of those new (x) 100 create another 100 (x) in another month. And the original (x) will constantly produce another hundred (x) as will the new 10% in each new batch of (x). And this process repeats for 12,000 years. I need to figure out how many (x) I will have at the end of that time. If you have any questions I'll do my best to answer them, thanks for your help!

This is for a book I'm writing, not a school problem, and I couldn't figure this out, and yahoo.answers was of no use either, so here I am.

 

[for]

nvm, forget it, the answer is infinite.

After one month:
1 => 100
10 = > 1000
100 = > 10000
1000 => 100,000

The period of 1 month NEVER ends, or so you state, so the replication of x's would just keep going on forever.

 

[soroban]

Hello, Bravoranger!

This is more than a simple exponential function.

I have a unit, which we'll call (x) for now.
So unit (x) starts out as 1 unit, but every month (x) creates another 100 (x).
In another month, 10% of those new (x) 100 create another 100 (x).
Each month, the original (x) will produce another hundred (x) as will 10% in each new batch of (x).

And this process repeats for 12,000 years.
I need to figure out how many (x) I will have at the end of that time.

I cranked out the first few months' populations . . .


Month 0: 1-unit

Month 1: The 1-unit creates another 100 units.
. . . . . . .Population: 101 units

Month 2: The 1-unit creates another 100 units.
. . . . . . .There are 100 new units.
. . . . . . .10% of them (10) creates 100 more units each.
. . . . . . .They make: 10 x 100 = 1,000 more units.
. . . . . . .Population: 1,201 units

Month 3: The 1-unit creates another 100 units.
. . . . . . .There are 1,100 new units.
. . . . . . .10% of them (110) creates 100 more units each.
. . . . . . .They make: 110 x 100 = 11,000 more units.
. . . . . . .Population: 12,201 units.

Month 4: The 1-unit creates another 100 units.
. . . . . . .There are 11,100 new units.
. . . . . . .10% of them (1,110) creates 100 more units each.
. . . . . . .They make: 1,110 x 100 = 111,000 more units.
. . . . . . .Population: 123,301 units.


I should be able the express the population in month m albegraically,
. . but my brain has turned to tapioca.

And you want this for 144,000 months? . . . Good luck!