Liquid yeast Starter Activator Smack Pack

Assuming you're talking about Wyeast, they recommend incubating '3-5 hours or more' after smacking. You certainly can wait days, and in fact may have to for older or poorly stored yeast packs, but it generally shouldn't be necessary. Is there somewhere you've read that recommends incubating for days, or is it just more a general question?

"Does the yeast colony double every 90 mins?"

Under ideal growth conditions and during the exponential growth phase, colony doublings can occur this quickly. However, when activating a smack-pack-type pitch (or anytime stored yeast is exposed to nutrient, such as with a starter or direct pitching), these conditions aren't met, so you can't assume that, in an hour and a half, you'll have twice the yeast you started with.

The smack-pack system is really meant more as a way to reduce the lag time (the initial phase after pitching where stored/unactivated yeast is 'waking up' and acclimating to its new, nutrient-rich environment and no real sign of fermentation is visible), which may last anywhere from less than an hour to a day or more. There is the added potential benefit of a modest increase in cell count but this is probably minimal (when directly pitching yeast [i.e. just slurry, no starter or activator] it is unusual to see an increase in cell number before 8-12 hours into fermentation, though you will see budding cells). Also, the nutrient pouch in the smack-packs is fairly small, so any increase in cell number may be limited by insufficient fermentable sugars, no matter how long you let it sit.