I'm trying to forecast the viral growth for a website I'm developing. I've arrived at some monthly growth rates I can expect per month, the difficulty is I'd like to model my growth per week instead.
Lets say I have these figures
Growth Rate Month 1 0.2 Month 2 0.1 Month 3 0.05 Month 4 0.025 Lifetime 0.375
What this means is that for every 5 new users to the site; they will invite another 1 new user in the first month. For every 10 new users, they will invite another user in their second month, etc. Looking at the pattern you can see that the growth rate decline is
50% each month. For the sake of simplicity we'll say the viral growth rate is 0 from month 5 onwards therefor a lifetime growth rate would be the sum of the first 4 months.
How does that translate to weekly growth rates, it's ok to make the assumption there's 4 weeks in a month.
Short version of the question (wrong)
I think what I need to calculate is (could be wrong), using month 1 as an example, how can I split
0.2 into four values where each is half (
50%) the value of the previous but the sum of all four totals
Short version findings
My theory towards approaching it in the short version is flawed, using that method I end up with results that look like this.
Growth Week 1 Week 2 Week 3 Week 4 Total Month 1 0.11 0.05 0.03 0.01 0.2 Month 2 0.05 0.03 0.01 0.01 0.1 Month 3 0.03 0.01 0.01 0 0.05 Month 4 0.01 0.01 0 0 0.025
(The values are rounded to 2dp)
This says that in week 4 there would be a viral growth rate of
0.01 whereas in week 5 there would be a growth rate of
0.05. Logically it shouldn't increase, each week should slowly decrease as if on a curve.
Would much appreciate any help on this, thanks.