Understanding linear and non linear change

The key question is how a quantity changes from one step to the next.
In a linear relationship it changes by a constant amount: you add (or subtract) the same number each time.
For example, starting at $100$ and adding $50$ each step gives $100, 150, 200, 250$ — a straight line.

In an exponential relationship the quantity changes by a constant factor instead: you multiply by the same number each time.
Starting at $100$ and multiplying by $1.5$ each step gives $100, 150, 225, 337.5$ — a curve that grows faster and faster.

You can tell them apart from a table.
If the values go up (or down) by the same amount each step, it is linear.
If they are multiplied by the same ratio each step, it is exponential.

A percent change is exponential, not linear.
If something decays by $8\%$ each hour, it does not lose the same number of grams each hour.
From $100$g it drops to $92$g (down $8$), then $92 \times 0.92 \approx 85$g (down about $7$) — the drop shrinks because it is always $8\%$ of a smaller amount.

Not every non-linear relationship is exponential.
A quadratic like $R = -40(h - 3)^2 + 80$ is also non-linear; its graph is a U-shape (or upside-down U), not a straight line.
The simple test for linear is always the same: does it change by a constant amount?

A table shows $x: 1, 2, 3, 4$ and $y: 2, 4, 6, 8$. Is the relationship linear or exponential?
Each time $x$ goes up by $1$, $y$ goes up by $2$ — the same amount every step.
A constant amount means the relationship is linear.

A phone is worth $\$100$, and each year it keeps $85\%$ of its value. Is the relationship linear or exponential?
Each year the value is multiplied by the same factor, $0.85$, rather than dropping by a fixed number of dollars.
A constant factor means the relationship is exponential.

An employee's salary rises by a fixed $\$2{,}500$ every year. Is this linear or exponential?
The salary increases by the same amount each year, $\$2{,}500$.
A constant amount means the relationship is linear.