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Equation 5 · Part 8 · The Metabolism of Civilization: Energy to 2100

subscript

c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}
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

The formal relationship goes back to Theodore Wright’s 1936 observation that aircraft manufacturing labor hours fell as a power-law function of the number of airframes already built, and Way et al. build their entire forecasting method on a stochastic version of it, fitted to more than fifty technologies’ historical cost and production records [ 1 ] . Written in its cleanest form, cost c at cumulative production (experience) z relates to a reference cost c0c_0 at reference experience z0z_0 by: c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}. where the experience exponent b sets the learning rate LR = 1 - 2^{-b} , the fractional cost drop for every doubling of z . Way et al.'s working version of the same relationship is…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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