After she premieres it on the Billboard Music Awards and it debuts at #1, it will stay there for 10 weeks until her second single (feat Rihanna) replaces it and keeps the top spot for 17 weeks, breaking the BEP record of consecutive weeks at #1.
She will debut her lead single at the 2013 Billboard Awards, where she will accept her award for Woman of the Year. The lead single will open up with 524K copies in the first week and about 30 million audience impressions. She will debut at #1 and stay there for about 2-3 weeks.
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I rather have her debut the song on American Idol's seasoning finale. She could both. Last year they were in the same week. The exposure.
The exposure. 
