Exponential Growth
A pattern where something grows faster and faster by repeatedly multiplying itself by a fixed number. đ
Kurze EinfĂŒhrung
Exponential growth is like a snowball effect, where numbers get bigger and bigger at an increasingly rapid pace. Imagine starting with one penny and doubling it every day - by the end of a month, you'd have millions! This pattern appears everywhere in nature, technology, and finance, making it one of the most powerful and important concepts to understand. đ±
HaupterklÀrung
The Multiplier Effect đ
In exponential growth, you multiply the current amount by the same number repeatedly. It's like a copy machine making copies of copies - if each copy makes two more copies, you'll soon have hundreds of papers.
Constant Growth Rate âïž
While the actual increases get larger, the rate stays the same. It's like having a savings account with 10% interest - the percentage doesn't change, but the actual money added grows larger each time.
Acceleration Over Time đ
The growth starts slowly but picks up incredible speed. It's like social media sharing - one person shares to 3 friends, then those 3 each share to 3 more, quickly reaching thousands.
Beispiele
- A viral video: Starting with 1 view, if each viewer shares with 2 friends who watch and share, it goes: 1 â 2 â 4 â 8 â 16 â 32 views, exploding in popularity. đ„
- Bacterial growth: One bacterium splitting into two every hour becomes 2, then 4, then 8, then 16, reaching millions in just one day! đŠ
- Folding paper: If you could fold a paper in half 42 times, its thickness would reach the moon! Each fold doubles the thickness, demonstrating the power of exponential growth. đ
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