I think many people get PLASMA half-life and BIOLOGICAL half-life mixed up. When we are talking about how long a dose of medication stays in the BLOODstream, we are talking about PLASMA half-life. Half-life is the amount of time it takes for a chemical substance to be reduced to HALF its original amount.

The plasma half-life of dex is 3-4.5 hours. For hydrocortisone, it is 1-2 hours. http://web.uct.ac.za/depts/mmi/jmoodie/h02tab.html

If you work through the math (1/2 x 1/2 x 1/2 x 1/2, etc., until the amounts become negligible), you’ll find that this means a dose of dex typically remains in the bloodstream about 16 hours, and a dose of hydrocortisone 6-8 hours.