The modeling process
Mathematical modeling turns a real-life situation into mathematics so it can be analysed. The steps are: (1) identify the variables and assumptions, (2) form the model (an equation or function), (3) solve it, (4) interpret the result back in the real context, and (5) evaluate whether the model is reasonable and improve it if needed.
Key formula
A linear model has the form $y = mx + c$, where $c$ is a fixed (base) amount and $m$ is the rate of change per unit of $x$. Other situations need other models — for example steady percentage growth is exponential.
Worked example
Worked example
A taxi charges RM4 plus RM2 per km. Let $d$ be the distance in km and $C$ the cost in RM. Form: $C = 4 + 2d$. Solve for a 15 km trip: $C = 4 + 2(15) = \text{RM}34$. Interpret: the trip costs RM34. Evaluate: the model is valid only while the per-km rate stays constant.
Remember
- Modeling is a cycle: form, solve, interpret, then evaluate and refine.
- State your assumptions — they set the limits of the model.
- Choose the model type (linear, quadratic, exponential) to match the situation.