Steady States

Where a recurrence settles

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

• $a_n = ka_{n-1} + c$ settles at $a^* = c/(1 - k)$ when $|k| < 1$.
• The gap shrinks by a factor $k$ each step; negative $k$ zig-zags.
• Repeated drug doses build up to a steady state.

Steps

1. Repeated doses
2. The steady level
3. Choose the dose
4. The general rule
5. A fish farm
6. Overshooting