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People often make the mistake of overthinking this. It doesn't take much time for a given (effective) load to trigger signals inside muscle cells to start growing. In a sufficiently deconditioned muscle, only 1 set of 10-12 reps is sufficient to cause measurable anabolic changes.
However, the more you train, the more resistant your muscle becomes to the training stimulus. We've know this for years, and recently we have some good research to demonstrate it by measuring signaling molecules in trained and untrained exercisers after a single bout.
So, the first solution to the problem of becoming resistant to the lifting stimulus is to create a more potent stimulus by lifting more weight. You can do this until you reach your strength limits.
Another solution is to lift the same amount of weight a bit longer by doing more sets and/or reps. This works to a point, but soon (2-3 weeks) will fail to produce growth once again.