Common Misconceptions

⚠️ Common Misconceptions

Misconception 1: "An exponential graph passes through the origin (0, 0)"

An exponential graph y = aˣ passes through (0, 1), NOT the origin. This is because any number raised to the power zero equals 1 (a⁰ = 1). The origin (0, 0) is on the curve only for linear graphs like y = mx, not for exponential graphs. This is one of the most commonly tested features — always mark the y-intercept at (0, 1) when sketching an exponential graph.

Misconception 2: "Exponential decay graphs eventually reach zero"

An exponential decay curve (0 < a < 1) approaches zero but NEVER reaches it. The x-axis is a horizontal asymptote. For example, in radioactive decay, the amount halves every half-life but never completely disappears — it just gets smaller and smaller without limit. This is why nuclear waste remains radioactive effectively forever from a practical standpoint. In exam sketches, always show the curve getting close to but not touching the x-axis.

Misconception 3: "Doubling time and compound growth are the same as adding a fixed amount each time"

Compound growth (exponential) multiplies by a fixed ratio each period, so the actual increase gets LARGER each time. Simple (linear) growth adds a fixed amount each time. For compound interest at 10% per year: £100 grows by £10 in year 1, then by £11 in year 2, then £12.10 in year 3 — the increase itself is increasing. This is fundamentally different from adding £10 per year, and the difference becomes enormous over long time periods.