When does an RC Transient period end?
When does an RC Transient period end?

Never. Its effects do diminish over time, so at some point the effect of the transient isn't relevant anymore.  For example, if the circuit settled to within 95% of its new value is good enough to consider the transient as "ended", then it takes 3 time constants.  If it needs to settle to 99% of its final level, then you have to wait 4.6 time constants.  For 99.9%, it's 6.9 time constants.

For this circuit the time constant or "Tau" is 80 micro Farads

No! The time constant has units of time.  Note that you multiplied Farads and Ohms to get it.  Since Ohms are not dimensionless, it should be obvious that the resulting product can't be in units of Farads.

or 80∗10−6

Again, No, the time constant is not dimensionless either.  Also, it seems you meant to say 10-6 in place of "10-6".