Oh this is hilarious how badly you're misunderstanding your own source. This is akin to 'peak oil' 30 years ago. The reserves listed in the article are about how much known reserves are capable of supplying AT FIXED MARKET RATES OF $130 - $230 / KG. And even then, those known reserves are sufficient for another century of mining. Where did you dig up '15 years' from? Reserves are sufficient to last us 'only' a century because there's no commercial benefit to more prospecting with the existing supply being that large.

Some choice quotes from YOUR linked source:

Further exploration and higher prices will certainly, on the basis of present geological knowledge, yield further resources as present ones are used up.

An orebody is, by definition, an occurrence of mineralization from which the metal is economically recoverable. Orebodies, and thus measured resources – the amount known to be economically recoverable from orebodies – are therefore relative to both costs of extraction and market prices. For example, at present neither the oceans nor any granites are orebodies, but conceivably either could become so if prices were to rise sufficiently. At ten times the current price*, seawater, for example, might become a potential source of vast amounts of uranium. Thus, any predictions of the future availability of any mineral, including uranium, which are based on current cost and price data, as well as current geological knowledge, are likely to prove extremely conservative.

They even SPECIFICALLY addressed your concern!

Of course the resources of the earth are indeed finite, but three observations need to be made: first, the limits of the supply of resources are so far away that the truism has no practical meaning. Second, many of the resources concerned are either renewable or recyclable (energy minerals and zinc are the main exceptions, though the recycling potential of many materials is limited in practice by the energy and other costs involved). Third, available reserves of 'non-renewable' resources are constantly being renewed, mostly faster than they are used.

Did you just try to google and link the first result or something? HALF THE ARTICLE IS SPECIFICALLY ABOUT HOW WE HISTORICALLY KEEP TALKING ABOUT RESOURCES RUNNING DRY, AND WHY THAT ENTIRE IDEA IS NONSENSE.