Lena, what business area shows the most potential for growth?
I can say, however, that if you're looking start a business and you're using business sector growth as the determining factor of what kind of business you open, you're barking up the wrong tree a bit.
Instead, focus on what you love. What are you passionate about? What would you do for free? What gets you excited? What could you talk about for hours? What topic brings out your strongest reactions? Once you've identified this, then you can look at market conditions to see the best direction for your business to take.
Doing anything else wouldn't get you the long term results you're probably seeking. Who would want to have a business in a growth industry that you really don't like working in?
If you're not convinced and you still want to focus on the industries with the greatest growth, a good place to start would be your public library. The resource librarian would be able to help you, or the United States Department of Commerce's web site at http://www.commerce.gov.