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Apple Inc.’s customers have downloaded more than 40 billion software applications from the company’s App Store, with almost half occurring last year as use of the iPhone and iPad surged.

More than 2 billion apps were downloaded in December, a record, Apple said Monday in a statement. Apple, with now more than 775,000 apps available for its iPhone, iPad and iPod Touch devices, said it has paid more than $7 billion to the developers of those applications.

Apple is counting on apps to help woo consumers who are choosing amid an increasing array of lower-priced tablets from competitors, including Google Inc., Amazon.com Inc. and Microsoft Corp. Apps can also help the iPhone compete against feature-laden phones from Samsung Electronics Co. and Nokia Oyj.

The growth in app-store users from 435 million in September, as well as the surge in downloads from 35 billion in October “could help allay some recent demand concerns,” Will Power, an analyst at Robert W. Baird & Co., wrote in a research report today. He rates the shares outperform with a target price of $750.

Shares of Apple slipped 0.6 percent to $523.90 at the close Monday in New York, a third straight day of declines after a 31 percent increase last year.

“Expectations are actually low and getting lower,” Ben Reitzes, an analyst at Barclays, wrote in the research report. “Many investors fear iPhone sales will be relatively flat this year and that there will be no move into TV that moves the needle.”