What does "time constant" mean?

In the case of conditioners, time constant reflects the response speed. In terms of a transfer function, it is expressed as OUT=INΩ(1-e EXP(-t/T)).
OUT: output, IN: input, e: natural log, T: time constant, t: elapsed time

When the elapsed time reaches the time constant, the e exponent becomes -1, and OUT becomes 63% of IN. When more time elapses, the exponent approaches -infinity, and OUT = IN.

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