Exponential Growth
A pattern where something grows faster and faster by repeatedly multiplying itself by a fixed number. π
Brief Introduction
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. π±
Main Explanation
The Multiplier Effect π
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 βοΈ
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 π
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.
Examples
- A viral video: Starting with 1 view, if each viewer shares with 2 friends who watch and share, it goes: 1 β 2 β 4 β 8 β 16 β 32 views, exploding in popularity. π₯
- Bacterial growth: One bacterium splitting into two every hour becomes 2, then 4, then 8, then 16, reaching millions in just one day! π¦
- 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. π