Time for some fun analysis.
$10,000 in 3 years.
Lets pretend that we were already at $500 for simplicity.
We need to rise $9,500 over 3 years = average of $3,166/year or $264/month
Of course we know that Bitcoin doesn't just rise a static amount each month, it tends to go through exponential bubble phases.
The previous bubble involved doubling every 2 weeks. (100, 200, 400, 800, 1200 - less than 4 doublings)
It is worth noting that MtGox was slow and shit during that bubble, and prevented it from going further.
The end of the bubble taking us to $10k should involve doublings of the following values over 2 week periods.
$10,000 (target!)
$5,000
$2,500
$1,250
$625
$10,000 is no magic number. It could go higher or lower, for example it could peak at $12,437, $23,299, or $8999. We don't know.
Due to our current trajectory I do not think $10,000 is high enough for a bubble, because $625 will be approached too slowly. If the bubble starts closer to $1,250 it is likely to go much higher than $10,000 (remember, just one extra doubling is $20,000).
Conclusion
For the bubble to stop at $10,000 we would need to start doubling at around our current price, which is not going to happen without a major game changing event (e.g. bank runs). Therefore I predict the next bubble to go over $20,000.
Seeing a value of 20,000$ would be great but I think that the next bubble will be lower than $10,000.