There are many challenges on Facebook, of the form:
for each day of N days you must perform a given task and on each day nominate one friend to also take part in the challenge
So, every time someone completes the challenge, they should have invited N friends to also take part in the challenge (one for each day).
Given the above, if x(t) is the number of people invited to the challenge at time t in days, how can I calculate t for any given x(t) assuming x(0) = 1?
For example, how can I calculate how many days it would take for 1 million invites to have happened?
I'm guessing this is going to involve a modified form of the exponential growth equation:
$$ x(t) = x_0 × (1 + r)^t $$
But as I understand, applying this only works if the N friends are all invited on the first day of a challenge...
The number of people doubles each day, so if we start counting with just you on day zero, there are $2^n$ people on day $n$. Given the number of people $p$, to find $n$ you take the base $2$ log. $n=\log_2 p$