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Equation 3 · Part 1 · Ten Failure Modes That Define Production Claude Code Use

Symbol T_50

T50(t)≈T50(t0)⋅2 (t−t0)/d,d≈7 months,T_{50}(t) \approx T_{50}(t_0) \cdot 2^{\,(t - t_0)/d}, \qquad d \approx 7\ \text{months},
T50T_{50}

What this part means

the task duration completable at 50% reliability at year t , METR’s fit is [displayed formula].

Its job in the formula

T5T_50 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

The organization’s headline trend — the task length completable at 50% reliability doubling roughly every seven months over six years of measurement — is worth writing as an explicit model rather than a slogan, because it is the empirical claim the section rests on: if T50(t)T_{50}(t) is the task duration completable at 50% reliability at year t , METR’s fit is T50(t)≈T50(t0)⋅2 (t−t0)/d,d≈7 monthsT_{50}(t) \approx T_{50}(t_0) \cdot 2^{\,(t - t_0)/d}, \qquad d \approx 7\ \text{months}.

The passage around this formula

…completable at 50% reliability doubling roughly every seven months over six years of measurement — is worth writing as an explicit model rather than a slogan, because it is the empirical claim the section rests on: if T50(t)T_{50}(t) is the task duration completable at 50% reliability at year t , METR’s fit is T50(t)≈T50(t0)⋅2 (t−t0)/d,d≈7 monthsT_{50}(t) \approx T_{50}(t_0) \cdot 2^{\,(t - t_0)/d}, \qquad d \approx 7\ \text{months}. with the organization’s own caveat that the exact doubling time d is sensitive to task selection and human-baseline methodology, even though the qualitative exponential trend is one they…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.