If the movement between the user groups remain the same, then in 10 years time, it will have stabilized on around 6% blackberry, 70% iphones, and 24% android (ignoring everyone going to "other smartphone os")
Unfortunately I must say that this method is flawed. The are two key implicit assumptions that break the whole thing. The lesser one first -
You are assuming that the sample you have taken is a good estimate of the true probabilities. You have assumed that the probabilities will remain the same. This latter assumption is the next problem.
you heard of the black swan concept? The future is predictable except for the unpredictable parts.
I say this because I too have been thinking about this and wondering what kind of model would be the least worst indicator since all predictors are poor the longer the timespan as a ratio of stability of system in study. I am thinking something inspired by the N body problem and swarm based optimization would be cool to look at. Alas, I have not the time to pursue this.
(Finally I got to use Markov chains! Code here for anyone interested: http://codepad.org/cstzwXbG )