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Equation 1 · Part 11 · From Origins to Frontier: A History of Claude Code and Agentic Development Tools

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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},
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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

A second, independently run measurement effort took a different approach: instead of asking whether an agent could solve one fixed set of tasks, it asked how long a task an agent could complete autonomously with 50% reliability, using human professional completion time as the unit. METR’s March 2025 study, compiled from 170 tasks and more than 800 human timing baselines across software engineering, cybersecurity and general reasoning work, reported that this “50%-task-completion time horizon” for frontier agents had been doubling approximately every seven months for six years running, and that the finding was robust to an order-of-magnitude error in the underlying measurements, which would…

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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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