Symbol n_i
is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Published equation contexts
Why this formula appears here
The pricing structure has a feature worth building a mental model around before it costs you money in production: it is not a marginal rate that blends smoothly as a request grows, it is a cliff. Every model’s documented price list carries two tiers — one for requests under 200,000 tokens, and a materially higher one, roughly double across the board, once a request reaches that threshold — and the higher rate applies to the entire request, not just the tokens past the line [ 1 ] . Written as a cost function of input tokens and output tokens against a threshold T = 200{,}000 , with low-tier prices , and high-tier prices , : . For…
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Symbol n_o
is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol p_o^L
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol T
T is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol p_i^H
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol p_o^H
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 6 · AI Industry
Actually Building with the Grok API
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
The pricing structure has a feature worth building a mental model around before it costs you money in production: it is not a marginal rate that blends smoothly as a request grows, it is a cliff. Every model’s documented price list carries two tiers — one for requests under 200,000 tokens, and a materially higher one, roughly double across the board, once a request reaches that threshold — and the higher rate applies to the entire request, not just the tokens past the line [ 1 ] . Written as a cost function of input tokens and output tokens against a threshold T = 200{,}000 , with low-tier prices , and high-tier prices , : . For…