Take a real-world situation, translate it into equations, then ask the equations to predict outcomes.
Drag the sliders
y = a·x + by = p·pow(q, x)
Building a model
- Identify what changes (the variable) and what depends on it.
- Choose a shape: constant rate ⇒ linear; growth proportional to size ⇒ exponential; up-then-down path ⇒ quadratic.
- Fit the parameters from known data points.
- Test the model's predictions against reality — and refine if it drifts.
Your turn
A tank holds 50 L and drains 4 L per minute. Write a model for volume V after t minutes, and find when it's empty.
A model is an approximation, not the truth. Watch where it breaks down — a linear 'drain' model gives negative volume past t = 12.5, which is nonsense. Know your model's valid range.
Common models
- Linear: y = mx + b — constant rate of change.
- Exponential: y = a·bˣ — growth or decay proportional to size.
- Quadratic: y = ax² + bx + c — projectile paths, area problems.