Higher Applications of Mathematics
Growth, decay and multiplicative change.
Check variables, formulae, model types, units, errors and assumptions.
Review Mathematical Modelling with adaptive feedback.
Method helper
Does the output change by a fixed amount each step?
Use a linear model.
Is there a starting fee plus a rate per unit?
Use y = mx + c and interpret the intercept.
Does the situation involve area, a turning point or a squared variable?
Use a quadratic model.
Is the amount increasing or decreasing by a percentage repeatedly?
Use an exponential model.
Have you been given a formula and values?
Substitute into the formula carefully.
Do you need to make one variable the subject?
Rearrange the formula one step at a time.
Are measurements rounded or allowed within a range?
Calculate tolerance or error.
Do the units look inconsistent?
Convert units and check dimensional sense.
Are you testing several assumptions or scenarios?
Use technology to compare model outputs.
Does the prediction seem unrealistic?
Comment on model limitations.
Modelling walkthrough 1
An electric bike is expected to depreciate by the same percentage each year.
Exponential decay is suitable when the same percentage is applied repeatedly.
Modelling walkthrough 2
An electric bike is expected to depreciate by the same percentage each year.
The factor controls the direction and size of the change.
Modelling walkthrough 3
An electric bike is expected to depreciate by the same percentage each year.
A depreciation model is an estimate, not a guaranteed resale value.
Technology and data connection
Next step
Use the learning notes to identify variables, assumptions and units, then try varied formulas, model types and reasonableness checks.