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> As more people are added to a project, the complexity of communication increases exponentially.

Doesn't it increase by n^2? as per the picture with the graphs?

Laypeople use "exponential" to mean "superlinear". It's fine, probably.

Brooks wrote that it was quadratic, so that seems to be an error in the summary.

Laypeople use “exponential” to mean “fast”, with what “fast" means varying by speaker and context.