Less than a week after Apple's (AAPL 0.52%) new iTunes Radio went live on Sept. 18 with the release of iOS 7, the company reports the service already boasts 11 million unique listeners.

Should Pandora (P) be worried? Definitely.

iTunes Radio. Source: Apple.

How many listeners did Pandora lose to Apple?
That seems to be the question of the day for Pandora investors. The stock plummeted today on the news of Apple's success in streaming radio. In just a few days, Apple has acquired an audience one-sixth the size of Pandora's 72.1 million active listeners. Gathering 11 million users in a few days is a large enough number in a short enough time to merit serious concern. Will this epic growth continue? How many of these listeners could be ditching Pandora?

And here is where the concern really starts to get serious: What if Pandora's growth story comes to a sudden halt? Slipping by on a slim profit with EPS of just $0.04 in Pandora's most recent quarter, the company's $24 share price certainly has future growth priced into the stock.

But is it realistic to expect Pandora to be able to grow its numbers going forward? While Apple added 11 million unique listeners in a few days, Pandora added just 16 million active listeners over the last 12 months.

And unlike Pandora, Apple has an existing ecosystem from which it can draw from, with already 200 million iOS devices running iOS 7. Assuming Apple could convince just 40% of those 200 million users to use iTunes Radio, that would already give Apple a larger listener base (80 million) than Pandora.

But even that estimate may be conservative. First of all, given the record adoption of iOS 7, its reasonable to assume Apple will likely eventually match its iOS 6 penetration of 93%. This would give the company a considerably larger pool to draw from. Second, Apple said this summer that the company has 575 million iTunes Store accounts linked to credit cards. This makes 80 million iTunes Radio listeners, especially after the company landed 11 million active listeners in a few days, seem like a very conservative estimate. If Apple eventually convinced 40% of users with an iTunes Store account to use iTunes Radio, the company would boast more than three times Pandora's current base of active listeners.

Pandora's response
Responding to the official announcement of iTunes Radio, the company seemed to show little concern for Apple's upcoming service. Though Pandora has recently said it will remove its 40-hour listening limit for free users, and it redesigned its iOS app last week, these actions may not be enough to thwart Apple's competition.

Fortunately, Pandora has a wave of increasing use of streaming radio working in its favor. But will Apple steal away current users' listening time faster than Pandora can gain new listeners? Sure, consumers can use both services -- but listeners will not be listening to both services at the same time. So there's a good chance a meaningful portion of Apple's new listeners will come at the direct expense of Pandora.

Making matters worse, iTunes Radio (along with an iTunes Match subscription) costs just $25 per year, compared to Pandora at $36, making the former an arguably a better value to consumers. Today's announcement from Apple only reinforces the fact that Pandora is a speculative investment at today's prices.