Tricky, Tricky, Problem of exponential growth, patch of lily pads the lake

Question

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Answer

---

We know that the lake is entirely covered on day 48.
So what was it the day before that?
If the lily pad patch doubles every day, the day before day 48, it was covering half the lake.
Right?
If you double half a pie you have a whole pie.
So how long would it take for the lily pad patch to cover half of the lake?
47 days.

The lily pad patch would cover half of the lake on day 47.

Tricky, tricky,

Day | Size of lily pad patch

----|----

1 | 1
2 | 2
3 | 4
...
46 | 2^46
47 | 2^47
48 | 2^48

Q and A

This is a problem of exponential growth, where the patch of lily pads doubles in size every day. Can you use the exponential growth formula to model this situation?

For example

A = P(1 + r)^t

where:

A: is the final amount
P: is the initial amount
r: is the growth rate
t: is the time in days

In this case, the initial amount (P) is 1, the growth rate (r) is 2, and the time (t) is 47. So, the final amount (A) is?

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