To solve this problem, we need to work backward from the given information and find the pattern of growth of water lilies.
Given information:
- The number of water lilies doubles daily.
- It takes 48 days to completely occupy the entire area of the lake.
Let's assume that on the last day (48th day), the entire area of the lake is covered by water lilies, and on the first day, there is only one water lily.
On the 48th day, the number of water lilies = 2^48 (since the number doubles daily) On the 47th day, the number of water lilies = 2^47 On the 46th day, the number of water lilies = 2^46 ... On the 1st day, the number of water lilies = 2^0 = 1
We know that on the 48th day, the entire area of the lake is covered, which means that on the 47th day, the area covered was half of the entire area.
Therefore, to occupy half of the entire area, it takes 47 days.
Similarly, to occupy one-fourth of the entire area, it will take 46 days. To occupy one-eighth of the entire area, it will take 45 days. ... To occupy one part out of 2^47 parts of the entire area, it will take 1 day.
Hence, to occupy just the first water lily (one part out of 2^48 parts of the entire area), it will take 0 days.
Therefore, it will take 47 days for the water lilies to occupy half of the entire area of the lake.