Doing a Google search using "exporting credit card rates" will provide you with several hits for you to explore your question. Here's an example of one of the hits.

Dear Dr. Don,
I have a credit card with an interest rate that is now up to 39.99 percent. Is this illegal? It started out lower but has really gotten up there.
Thank you
Loren Loan

Dear Loren:
Your credit card agreement gives the provider the right to raise the interest rate on your credit card under certain conditions, such as late payments on any loan, or for any reason at all as long as it provides the notice required in the agreement -- typically 15 days. This Bankrate feature shows the ways creditors look for an excuse to raise your rates.

Consumers expect protection from their state's usury laws, but the governing law is the maximum interest rate permitted in the bank's home state. Credit card companies headquarter in states with high rates or no maximum rates so they can have more flexibility in setting rates.

A 1978 Supreme Court decision in Marquette vs. First Omaha Services confirmed the legality of nationally chartered banks exporting the terms of their cards to states where the laws regarding interest rates restricted such practices. This Bankrate feature has more on this practice.