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Equation 3 · Part 4 · Cities Are Organisms That Refuse to Die: Urban Evolution to 2100

Symbol N^β

Y(N)=Y0 NβY(N) = Y_0 \, N^{\beta}
NβN^{\beta}

What this part means

N^β is an input to the expression that computes the quantity on the left.

Its job in the formula

N^β is an input to the expression that computes the quantity on the left.

The passage around this formula

In 2007, Bettencourt, Lobo, Helbing, Kühnert and West published a cross-sectional analysis of American metropolitan statistical areas that has since become the standard citation for the claim that cities obey scaling laws. Measured against city population, quantities tied to innovation and economic output scale superlinearly — new patents scaled with an exponent of 1.27, inventors 1.25, private research and development employment 1.34, GDP in a range of 1.15 to 1.26, total wages 1.12, even serious crime 1.16 — while quantities tied to physical infrastructure scale sublinearly: length of electrical cable 0.87, road surface 0.83, gasoline stations 0.77, gasoline sales 0.79 [ 1 ] . In the…

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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.