Bernoulli’s Inequality

Growth beats a straight line

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Bernoulli: $(1 + x)^n \ge 1 + nx$ for $x \ge -1$.
• Compound growth always beats simple growth.
• The line 1 + nx is the tangent to the curve at x = 0.

Steps

1. Compounding versus simple
2. Curve over line
3. A quick bound
4. A shrinking bound
5. A guaranteed doubling
6. Why x ≥ −1?