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? [duplicate]

Starting with 8 pcs. is like 3 days have gone by. So 27 days remain.

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.

Another way to look at it is to work backward.

First just consider the one lily pad. After $29$ days it covers half the pond. After $28$ days a quarter of the pond. After $27$ days an eighth of the pond.

So after $27$ days eight lily pads would cover the whole pond.

I think that, intuitively, the answer should be less than $30/4$ since it is increasing at an exponential rate.

Lily pad doubles in size every day, so it is increasing as a geometric progression. $$\begin{array}{c|c|c|c|c|c|c|c|c} \text{n-th day}&1&2&3&4&\cdots&26&27&28&29&30\\ \hline \text{size of $1$ lily pad}&1&2&2^2&2^3&\cdots&2^{25}&2^{26}&2^{27}&2^{28}&\color{red}{2^{29}} \end{array}$$

If you start with $8$ lily pads, each doubling on its own, then: $$\begin{array}{c|c|c|c|c|c|c|c|c} \text{n-th day}&1&2&3&4&\cdots&26&27&28&29&30\\ \hline \text{size of $8$ lily pads}&2^3&2^4&2^5&2^6&\cdots&2^{28}&\color{red}{2^{29}}&2^{30}&2^{31}&2^{32} \end{array}$$ Because when each of $8$ lily pads keeps doubling per day, the $8$ lily pads increase $8$ times faster in size altogether than that of one lily pad. So, you must multiply the size of one lily pad on any day by $8=2^3$ to find the total size of $8$ lily pads.

As this source informs, the Giant Water Lily may grow as large as $8$ to $9$ feet ($2.4-2.7$m) in diameter.