Reactive Rates of Bromination of Alkyl-Substituted Alkenes

Here is my question.  I am working through this and some other problems, and want to compare what I do against what someone who knows a lot more than me on this subject, does.  

Please don't do this problem if you are:
1.  Planning on copying and pasting something from a website (yes, I've had people do that to me here) that doesn't even begin to answer my question, and I've probably already seen anyway.  
2.  Aren't confident in your answer.

Sorry to sound rude, but I've paid for org chem advice on this site that was wrong more than once (or copied lazily and inappropriately from a website, as mentioned), so I'd like to avoid that if possible.  Thanks for your help.

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PROBLEM:

Rationalize the following relative reaction rates in terms of the accepted mechanism for bromination of alkenes (for each substrate, explain why its rate is faster than the one above and slower than the one below).


Reactive Rates of Bromination of Alkyl-Substituted Alkenes by Bromine in Methanolic Sodium Bromide at 25 degrees C:

Alkene                                      Relative Rate
-------------                               -----------------

Ethene                                               1
Propene                                           61
trans-2-butene                             1,700
cis-2-butene                                2,600
2-methylpropene                         5,400
2-methyl-2-butene                   130,000
2,3-dimethyl-2-butene           1,800,000