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Equation 7 · Part 1 · AI Inference Economics in Practice: An Advanced Technical Guide

Symbol R^*

R∗≈1.28R^{*} \approx 1.28
R∗R^{*}

What this part means

R∗R^* is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

R∗R^* is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

is exceeded. At Anthropic’s five-minute rate, w = 1.25 and R∗R^{*} ≈\approx 1.28 : the prefix pays for itself starting with the first read after the write, matching the break-even Anthropic’s pricing page states for that duration [ 6 ] . At the one-hour rate, w = 2 and R∗R^{*} ≈\approx 2.11 , matching the stated two-read break-even for that window [ 6 ] . The formula’s use is computing the same threshold for a w and r that are not round numbers, and deciding, before writing code, whether a prefix’s expected reuse clears the bar for the TTL about to be selected.

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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

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