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Equation 1 · Part 2 · From Origins to Frontier: A History of Claude Code and Agentic Development Tools

Symbol t

T50(t)  =  T0⋅2 (t−t0)/τ,τ≈7 months,T_{50}(t) \;=\; T_0 \cdot 2^{\,(t - t_0)/\tau}, \qquad \tau \approx 7 \text{ months},
tt

What this part means

the time or time index used in this relationship.

Its job in the formula

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

where T50(t)T_{50}(t) is the length of task, measured in human-hours, that a frontier agent could complete autonomously with 50% reliability at time t .

The passage around this formula

…trend as a simple exponential makes its shape explicit: T50(t)  =  T0⋅2 (t−t0)/τ,τ≈7 monthsT_{50}(t) \;=\; T_0 \cdot 2^{\,(t - t_0)/\tau}, \qquad \tau \approx 7 \text{ months}. where T50(t)T_{50}(t) is the length of task, measured in human-hours, that a frontier agent could complete autonomously with 50% reliability at time t . This is an empirical regression over six years of a specific evaluation methodology, not a law of nature, and METR’s own reporting is explicit that the trend could bend in either direction; it is included here because it is the clearest available answer to “how would you know if agentic coding…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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