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Equation 1 · Part 10 · From Origins to Frontier: A History of Claude Code and Agentic Development Tools

subscript

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},
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

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.