A.0.5—Powers, exponentials and logarithms

Powers describe repeated multiplication; exponentials model multiplicative change; logarithms reverse exponentiation and turn products into sums. Identify which quantity is changing before choosing a form.

For growth or decay, compare ratios across equal time intervals. A logarithmic transform is useful when a relationship becomes linear after taking logs.

A tenfold increase changes log₁₀(x) by 1, while doubling changes it by log₁₀2, not by 2.

A logarithmic scale compresses differences; equal distances on the graph do not mean equal absolute changes.