People that worry about the peaking of global oil supplies often use symmetrical curves as simple models for how production will peak and then decline, with logistics and Gaussians being popular choices. This goes back to M. King Hubbert (and I've done some of this myself). The United States is the poster child for this kind of analysis, since this region was the first to be developed at scale and production peaked in 1970.
However, it seems increasingly clear that the US production curve is far from symmetrical (perhaps driven by higher prices since the 1970s, and especially in the 2000s). Using data from the EIA for production and reserves, we can see that the decline side is slower than the growth side for both:
Here I have expressed the reserves on the right scale in millions-of-barrels-per-day-years (ie the number of years that the the current reserves would permit you to produce at a steady rate of one million barrels/day). Production is on the left scale in mbd.
You can see the noticeable slowing of decline in both production and reserves in the last decade.
If you look at the ratio (reserves/production, often abbreviated to R/P) you can see that it declined initially from very high values, reached a low in the 1980s, but has improved slightly in the last couple of decades:
We have been running with about 10 years worth of reserves for fifty years now. The general picture seems to be, that although we are scraping the bottom of the barrel - hunting for oil in very deep water in the Gulf of Mexico, fraccing very tight rocks to squeeze oil out by the drop, pumping in CO2 to loosen up the gunk - the bottom of the barrel is a more productive environment than one might have feared. Thus overall decline rates are low.
To see the asymmetry of the production curve more clearly, here I plot both the before and after peak periods on the same scale:
You can see that production now, forty years after the US peak, is pretty much twice as high as it was forty years before the peak (nor can this be written off as an artifact due to Alaska, which is down to 600kbd these days).
If global oil production behaves like the US, we might expect peak oil to take the form of a long plateau and a slow decline, which would tend to maximize hope for eventually successful adaptation (albeit with quite a bit of pain along the way).