Practice anything and you get faster — but not evenly. The first hour buys a huge gain; the thousandth hour barely moves the needle. Time-per-task falls as a POWER of the number of tries, which on a log-log plot is a dead-straight line. Slide the practice and watch the curve bend, then straighten.
The power law of practice: T(N) = a·N^(−b), the time to do a task after N repetitions. Because it is a power law, taking logs gives log T = log a − b·log N — a straight line of slope −b on log-log axes, the signature that distinguishes it from mere exponential decay. The instrument plots both the raw curve and the log-log line. A fail-loud self-check throws unless the measured log-log slope equals −b exactly and T is strictly decreasing — diminishing returns, quantified.
Whether learning is truly a power law or a sum of exponentials is a real debate (Heathcote 2000); the power law fits aggregated data well and is the classic form (Newell & Rosenbloom 1981). The a·N^−b arithmetic and its log-log line are exact.