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Comment by solonagathon | Hacker News Reader

How would you calculate the timeframe until steady number of subscribers is achieve d?

If M is the number of months then (since you can't have a fraction of a subscriber) you will be in steady state when

Y * X^(M - 1) < 1

so once

M > 1 - (ln Y / ln X)

Wouldn't it always require an infinite amount of time?

You're summing a series of:

    0.5^n * x

From n = 1 to n = infinity

Only if you can have a fraction of a subscriber, otherwise there will a finite number of months after which you will attain steady state.