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A logarithmic scale is useful if you care more about the variations in data for small numbers than those for large numbers. An exponential scale should be useful for the opposite use case—i.e., when smaller variations in larger numbers are important.
Gnuplot has builtin support for scaling the axes logarithmically. Does it have support for exponential scaling? If so, what is the syntax to use that? If not, what is there an elegant workaround?
There is no builtin support for exponential scaling. You can plot the graph
using (exp($1)):2, though.