Data & measurement
Continuity metrics emphasize intergenerational transmission, corpus completeness, and structural stability. Keep cohort definitions fixed across measurement waves. Symbols: t (Half-life time (in years or generations)); c (Decay constant (annual retention rate, 0-1)); ln (Natural logarithm). Log instrument versions, sample frames, and cleaning rules whenever estimates are refreshed so longitudinal comparisons stay valid.
Solution & proof
Conceptual summary: How long it takes for half of a set of native Kifuliiru words to fall out of active use. This predicts when vocabulary might "expire" if current trends continue. Treat this as a measurement recipe: map each symbol to an empirical quantity, substitute estimates, and simplify with ordinary algebra (including logarithms, min/max caps, or piecewise branches where shown). Where limits or integrals appear, approximate with discrete sums on cohorts or time steps when closed forms are impractical. Interpret the result against thresholds in the cited source and report uncertainty on inputs.
Worked examples and interactive charts now live on their own page.
Open the playground to test sample values, review worked scenarios, and explore how this formula behaves across multiple cases.
Variables
Variables
| Symbol | Description |
|---|---|
t | Half-life time (in years or generations) |
c | Decay constant (annual retention rate, 0-1) |
ln | Natural logarithm |
Source & tags
Source
ALL_FORMULAS.md — Continuity