One lily pad, doubling in size every day, covers a pond in 30 days. How long would it take eight lily pads to cover the pond? 
A lily pad sits on a pond. It doubles in size every day. It takes 30
  days for it to cover the pond. If you start with 8 lily pads instead,
  how many days does it take to cover the pond?

I think that the answer is $27$, but I don't really think that makes sense intuitively. I think that, intuitively, the answer should be less than $30/4$ since it is increasing at an exponential rate.

Hint $\#1$:
At the end of the $30$ days with one lilypad, the doubling means that the lilypad now encompasses the area of $2^{30}$ of the original lilypads.
In that light, starting with $2^3 = 8$ lilypads and each one doubling in size per day, how many doublings will it take for you to get to $2^{30}$?
(I know you've already solved this, I just think rewording/reframing the question might make it a bit easier to grasp on the intuitive level.)

Hint $\#2$:
If that doesn't help ease your intuition behind your answer (which to my understanding is correct), keep in mind that starting with $8$ lilypads is basically no different than your first scenario after $3$ days. Sure, you have more lilypads, but since each doubles in size, it's no different than one lilypad of the same size as those $8$ put together then doubling. The number of lilypads differs, but we're focused on the total area encompassed.
