Growth, Decay and e

The function that is its own slope

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

• $\dfrac{d}{dx}e^x = e^x$, where $e \approx 2.718$.
• $\dfrac{dy}{dt} = ky$ has solution $y = y_0 e^{kt}$.
• Doubling time or half-life: $T = \ln 2 / |k|$.

Steps

1. Tune the growth rate
2. Solving dy/dt = ky
3. Bacteria
4. The rule of 70
5. Half-life from the rate
6. Radioactive iodine