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Equation 3 · Part 9 · Ten Failure Modes That Define Production Claude Code Use

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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},
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

It is intuitive to expect an agentic session to improve as it accumulates context about a task. The measured pattern runs the other way. METR’s time-horizon research tracks the length of task — measured in how long a skilled human would take — that a frontier model can complete autonomously with a given reliability, and finds current frontier models near 100% success on tasks taking a human under four minutes, collapsing to under 10% success on tasks taking more than about four hours, with Claude 3.7 Sonnet reported specifically among the models exhibiting this drop-off [ 13 ] . The organization’s headline trend — the task length completable at 50% reliability doubling roughly every seven…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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