Spooling up times
You are aware (of course) that there is an engine certification requirement for slam acceleration response. JAR-E 745, IIRC, :
For all Engines, an increase can be made from 15% of the rated Take-off power or thrust, to 95% of the rated Take-off power or thrust in a time not greater than 5 seconds. A longer time may be accepted if properly justified. This power or thrust response must occur from a stabilised static condition using only the bleed air and accessories loads necessary to run the Engine
The requirement is for a sea level test, and "most" modern turbofans meet it.
As operation altitude increases, the speed of response does reduce (to prevent stall / surge).
Hope this helps...