← All parts of this equation

Equation 4 · Part 8 · Seventy-Five Thousand Generations of E. coli, and Counting

superscript

wopen(t)=1+a tβw_{\text{open}}(t) = 1 + a\,t^{\beta}
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

which approaches a fixed value of 1 + a/b as t grows without bound, and wopen(t)=1+a tβw_{\text{open}}(t) = 1 + a\,t^{\beta}. for an exponent β\beta between 0 and 1, which keeps rising — more and more slowly, but without any asymptote — for every value of t . Wiser and colleagues derived the second form theoretically from a model combining clonal interference with diminishing-returns epistasis among beneficial mutations, and reported that across 50,000 generations of real data, “mean fitness appears to increase without bound, consistent with a power law” [ 2 ] . The decelerating rate that Lenski’s 1991 paper had already observed over the first 2,000 generations turns out to be compatible with no ceiling at all: a…

Read this part in the article →

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.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the surrounding passage

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