Here’s a link to Apple’s official sales numbers. The first column shows the quarter that we’re interested in, labeled Q1’15. Note that total iPhone sales went from 51 million units from Q1’14 (a year ago) to 74 million units this last quarter. That’s a 45.9% increase.

Here’s Tim Cook, responding to an analyst question:

You can see from the March guidance that we’ve given that we’re incredibly bullish about iPhone going forward. We believe it’s the best smartphone in the world, our customers are telling us that, the market is telling us that. We’re doing well in virtually every corner of the world, and so we’re very bullish that it does have legs. I would point out that only a small fraction of the installed base has upgraded, so there’s a lot more people within the installed base, but I would also point out that we had the highest number of customers new to iPhone last quarter than in any prior launch. And also that the current iPhone lineup experienced the highest Android switcher rate in any of the last three launches in any of the three previous years. We didn’t look back to the other years, I don’t know about those.

First, “only a small fraction of the installed base has upgraded”. Not sure what that small fraction is, but this is followed by, “we had the highest number of customers new to iPhone last quarter than in any prior launch” and “the current iPhone lineup experienced the highest Android switcher rate in any of the last three launches in any of the three previous years”.

These are solid indicators all the way around. There is still lots of room for growth within the installed base, and the potential market for iPhones continues to grow outside the installed base. Some of that growth is coming at the expense of Android cannibalism in existing markets. But we also know that Apple is making headway in establishing new markets, especially in China.

These are remarkable results. Apple might just survive.