Minecart boosting was removed in Minecraft Beta 1.6.
This answer is only relevant for versions of Minecraft built prior to that revision, accessible using the Minecraft Launcher's Time Machine functionality.
It depends on whether the cart has a rider (cow, chicken, player) or not.
Now, first some definitions.
The type of booster used is a speed and momentum resetting booster, to ensure fair and reproducable results.
This is a booster with a length of 1
and here a booster with length 11
The bottom bedrock layer shown in these images is layer 0, the void is directly below.
the track going up shown on the left side is the actual track going up.
The results are in and show that an empty cart needs a booster of 18 long, while a cart with a rider in it will need a booster of 5 long to reach beyond the top of the map. (altrough, a booster of 17, with an empty cart, reaches sufficiently close.)
Now, for the booster lengths below these numbers, the following results has been obtained:
Raw data (height reached, booster length is position in list, where the first has a length of 1 as shown above.):
empty cart: 6 12 17 25.5 31 41 47 57 63 72.5 79 88 93.5 103 109 119 125
with rider: 6 25.5 37 66
I'm now trying to make some sense of the results for the empty cart, I don't think I have enough data points to make something for the cart with a rider.