In my view, the industry practice of fitting hyperbolic curves to data on declining productivity, and inferring lifetimes of 40 years or more, is too optimistic. Existing production histories are a few years at best, and thus are insufficient to substantiate such long lifetimes for wells. Because production declines more steeply than these models typically suggest, the method often overestimates ultimate recoveries and economic performance (see go.nature.com/kiamlk). The US Geological Survey's recovery estimates are less than half of those sometimes touted by industry.
In short, yes you can fit a line to data points (i.e. production over time; do check out the link in Hughes' quote) to model or predict how predict how production will change over time. But this does not necessarily make these predictions valid or accurate! These 'hyperbolic curves' (see bottom graph from the above link) are often calculated from only five years of data, but used to predict production some 40 years down the line. And what's more, these predicted values (i.e. points on the fitted line) are not spot-on, but have a confidence interval, a range of uncertainty in which a predicted value could be found. This interval increases drastically the further off in time you are predicting.
The point: we shouldn't be so confident in fracking and shale reserves to help solve the U.S.'s energy problems. In fact, we should be confident (and conservative) assuming they won't solve anything for anyone except people making money off them (and even then, only in the short term).
I've commented on this blog before about the importance of understanding the statistical methods one employs. In the present case, industry 'specialists,' whether they understood line fitting or not, erroneously used statistics to predict optimistic outcomes for US energy production. And the US government and public were eager to swallow this up hook, line and sinker.
The comment (sorry it's behind a paywall)
Hughes, J. (2013). Energy: A reality check on the shale revolution Nature, 494 (7437), 307-308 DOI: 10.1038/494307a