There are deferring opinions but here is what I can add
Cells to Pitch = 1 Million x milliliters wort x degrees Plato
The 1 million can be between .75 Million to 1.25 Million depending on the source of information.
Now in useful US units that is
Cells to Pitch = 0.5 to 0.7 Billion x Gallons x Specific Gravity Points [Palmer suggests 0.5 and White suggests 0.70]
For a lager, fermented at colder temperatures the general wisdom is to double the pitch rate.
So in a 5.5 gallons of 1.050 sg Wort
Cells to Pitch = .6 B x 5.5 x 50 = 165 Billion Cells. The really problem is how long it takes count to even 1 Billion ! ! !
So continuing on to usefulness.
There are 100 Billion in a Wyeast Smack Pack and in the White Labs vial. There is about 14 ml of very clean yeast slurry in the bottom of the White Labs vial so there are about 8 Billion cells per milliliter of "pure" yeast slurry.
So we need 165 Billion cells for a 5.5 Gallon batch of wort and the largest size we can buy only has 100 Billion cells.
Don't worry, the yeast love to grow. You can either pitch the 100 cells as is or create a starter batch a grow some more yeast. The problems are the yeast begin to die off as soon as they leave the factory and by the time you pitch several weeks or months after you get the yeast the less there is. And if you order online in the summer the yeast has to suffer through some intense heat. And during the growth stage you get some pretty awful favors, just ask anyone who ever tasted a starter.
There are a lot of opinions (and in my opinion, misconceptions on starters). The things that I think I know are yeast love to reproduce and they stop reproducing at about 200 million per ml of wort. They love oxygen and agitation (stirring). So to get 150 Billion cells I need a minimum 750 ml of starter. It really doesn't matter much how much yeast you start with as long as you have thoroughly oxygenated the wort and you continuously stir it (magnetic stir plate); the yeast will grow to the maximum concentration.
Yeast will double about every 2-4 hours, so the number of cells is Cell at Start x 2^doublings. (The ^ is the exponent or raised to)
Assume 50 Billion cells to start x 2^2 = 200 Billion; so 2 doublings are required at 4 hours each so about 8 hours.
Assume 1 Billion cells to start x 2^8 = 256 Billion; so 8 doublings x 4 hours = 32 hours.
In both cases the maximum yeast growth will be limited by the 200 million cells / ml concentration.
You can try your own experiment. Start with one smack pack or one vial. Get two starters at 750ml. Split the contents of the yeast package into one with 90% and the other with 10% of the yeast slurry. Let both starters ferment out for 3-4 days. Let the yeast settle to the bottom and see if you about the same yeast in each. I think you will be close.
All the best, D