Solve the lily pad lake riddle and experience the effect of exponential growth. Learn to think inventively to get the solution.
The Lily Pad Lake Riddle
There is a patch of lily pads in a lake. 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 the lake?
Solution to the Lily Pad Lake Riddle: Step by Step Reasoning
At first glance, it seems like a straightforward question about exponential growth. However, the key is to understand the nature of the doubling process and how it relates to the time to cover the lake.
Breaking Down the Information
- Initial Condition: There's a patch of lily pads in a lake.
- Growth Pattern: Every day, the patch doubles in size.
- Total Time to Cover the Lake: 48 days.
We need to find out how long it takes for the patch to cover half the lake.
Visualizing the Growth
Since the lily pad patch doubles in size each day, its growth follows an exponential pattern. This means that each day's size is twice the size of the previous day.
Let's denote:
- Day 0: Initial size (let's call it size S).
- Day 1: Size = 2S.
- Day 2: Size = 4S.
- ...
- Day 48: Size covers the entire lake.
Do I go on calculating the size of each day's covered area till the 47th day? This is not a sensible way to solve a puzzle! Too laborious and crude way of thinking.
Let me start with the known facts, and what I need to find out.
I know for sure, on the 48th day, the lily pads will cover the entire lake. And I only need to find out how much of the lake the lily pads will cover on the 47th day. Right?
This shows me the right way to approach the problem.
Working Backwards
Given that on Day 48, the patch covers the entire lake, we can work backwards to find out when it covers half the lake.
- Day 48: Entire lake covered (size = L).
- Day 47: Since the patch doubles each day, on Day 47, the patch must have been half the size of Day 48.
Therefore:
- Day 47: Size = L / 2.
One day before completely covering the lake, the patch measured half the lake’s size; even then, the lake creatures won’t realize that sunlight and oxygen, vital for life, would be blocked forever the next day.
Conclusion
Based on this reasoning, it takes 47 days for the lily pad patch to cover half the lake.
Verification
To ensure this makes sense, let's verify with smaller numbers.
Example:
- Suppose it takes 5 days to cover the entire lake.
- Day 5: Entire lake covered.
- Day 4: Half the lake covered (since it doubles on Day 5 to cover the entire lake).
- Day 3: One-fourth of the lake covered.
- And so on.
This pattern holds true, confirming that the patch covers half the lake one day before it covers the entire lake.
Ultimate Answer
It takes 47 days for the lily pad patch to cover half the lake.
Visual effect
Experience visually the effect of exponential growth. Instead of 48 days of covering, the lily pads cover the entire lake surface on the 5th day with surface on the days before, the 1st, 2nd, 3rd and 4th day, colored green.
The Doomsday Metaphor: Climate Change by Exponential Growth
The lily pad lake serves as a metaphor for the consequences of exponential growth in a limited world, reminding us of the delicate balance in nature.
When the lily pad lake is covered by the pads fully, no organism living peacefully in the lake will survive.
The lake of limited size is our dear earth and the lily pads are all the dozen plus consequences of climate destabilization to human system destabilization crises increasing in their adversity at exponential rates. Being vast and complex, none of the crises can be slowed down or stopped when the bend of the natural exponential curve is crossed.
We have long crossed it.
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