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Linear vs. Exponential Growth

There are two main ways quantities increase:

Linear Growth (Additive): Adding a fixed amount each step.
- Example: Walking up a ladder. Each step adds 20 cm to your height.
- Sequence: 20, 40, 60, 80…
Exponential Growth (Multiplicative): Multiplying by a fixed amount each step.
- Example: Cell division or folding paper. Each step doubles the previous value.
- Sequence: 1, 2, 4, 8, 16…

The Paper Folding Experiment

Let’s look at the thickness of paper (assumed $0.001$ cm) as we fold it.

Folds ( $n$ )	Calculation	Thickness ( $2^n \times 0.001$ )	Comparison
0	$2^0$	0.001 cm	Sheet of paper
10	$2^{10}$	$\approx 1.02$ cm	Notebook
17	$2^{17}$	$\approx 131$ cm	4-year-old child
27	$2^{27}$	$\approx 1.3$ km	Small Mountain
30	$2^{30}$	$\approx 10.7$ km	Cruising altitude of jets
46	$2^{46}$	$\approx 70,368,744$ km	Distance to Moon (approx)

Tip

Key Insight: Linear growth adds up slowly. Exponential growth starts slow but explodes very quickly. This is why just 46 folds can reach the moon!

Exponential Growth

Linear vs. Exponential Growth

The Paper Folding Experiment

Visualizing the Difference