SINCE its stockmarket flotation in America earlier this year, Facebook has seen its share price plunge as sceptical investors have dumped its stock. But at least one thing has continued to rise: on October 4th the giant social network revealed it now has one billion active monthly users, twice as many as in July 2010. Mark Zuckerberg, the firm’s boss, crowed that this puts it in the same pantheon as firms such as Coca-Cola and McDonald’s, which also have vast, global audiences.

Indeed it does. But Facebook still faces big questions that need to be answered more clearly for its share price to start heading in the same direction as its membership numbers. One is how it intends to earn more money from advertising in the mobile arena. The company revealed that it now has some 600m mobile users, which is another impressive number, and its acquisition this year of Instagram, a picture-sharing service for smartphones, has beefed up its capabilities in the fast-growing mobile market. But it is still casting around for effective advertising formats.

Another important question is whether the company can find new ways to share even more data about users’ online lives with advertisers without prompting a massive backlash over privacy issues. Facebook is already under intense scrutiny from regulators in America and Europe over things such as its use of facial recognition software. It also needs to show that it can diversify its sources of revenue. This is why it is experimenting with things such as allowing users to buy and send physical gifts via its service.

The social network will need to tackle these and other challenges if it is to keep growing steadily and profitably—and get its share price back up. But it can certainly be forgiven for taking time out to boast about some impressive numbers, which show that it is still a remarkable company. Its more than one billion users have uploaded almost 220 billion photos. And they have clicked the “like” button more than a trillion times since it was introduced in 2009. It is now up to Mr Zuckerberg and his team to get investors to like Facebook as much again.