2 · IB Maths AA
Exponential models
Adjust A, k and c in y = A·e^(kt) + c to fit a set of data points, drag the points to make your own data, and see how the half-life or doubling time depends only on k.
Drag a red point to move it. Keyboard: focus the graph, ←/→ select a point, ↑/↓ move it, Shift+←/→ move it in t.
y = A·e^(kt) + c
T½ or T₂ = ln 2 ÷ |k|
T½ or T₂ = ln 2 ÷ |k|
Try this
- With “Cooling coffee”, set c to the room temperature first, then adjust A and k by eye until the RMS residual is below 2. Compare with “Best fit”.
- Keep k fixed and change A and c: confirm the half-life does not change. Then double k and check that T½ halves.
- In “Bacterial growth”, drag the last point upwards and watch how much the best-fit k and doubling time change because of one point.
Common error: when a model has a vertical shift c, it is y − c (not y) that halves every half-life, so with cooling you must subtract the room temperature before using ln 2 ÷ |k|.