Quick questions on Choosing between linear and non-linear models for HSC Maths Standard 2

Given a table of $(x, y)$ pairs with $x$ equally spaced:

Sometimes a small dataset fits multiple models reasonably well. The question will normally guide you (for example, "the growth percentage is constant" tells you exponential). If asked to compare fit, plot residuals: the better model has smaller residuals across the dataset.

A regional Australian town population in $2020$, $2021$, $2022$, $2023$, $2024$ is $8000$, $8240$, $8487$, $8742$, $9004$.

A \50$pizza order is shared among$n$people. Cost per person is$\frac{50}{n}$. Products$n \times c = 50$ are constant by definition. Reciprocal model.

Linear has constant first differences. Exponential has constant ratios. Both can look similar over a small range of $x$.

Whenever the problem mentions a fixed total split into variable parts, the model is reciprocal.

A linear model in dollars with $x$ in years is fundamentally different from a linear model in dollars with $x$ in months. State units.

If linear fits well, do not fit a quadratic just to use more algebra. The right model is the simplest one that fits the data. :::