Half-life decay???? I would say
not at first. Despite all the problems in the system, I think that there is enough strength in it to prevent the sudden death.........at least at first.
My best guess is that the economic path down will be a bit like the down side of a 'bell-curve'* with a slow decline at first, but one that gathers pace and falls sharply, followed by a curving out at the bottom. I think we will see an initial 'gradual' decline in economic activity - you know like GM laying off workers, or the housing market spluttering along for a while. This will increase the downward pressure on the economy. The economy will be able to withstand the pressure for a while (and may be more robust than most of us think). Some of the pressure would be let off by people conserving etc**, but I am sure that this will not be enough and the overall pressure will grow. Then BANG.

At this point then we might see a very steep slide---possibly the half-life secenario will be a good case, OR then we will see the cliff/fall/collapse that many predict.
I am clueless as to how much pressure the economy can stand, but where I am I am doing as much as I can to conserve/promote effeciency, so letting off some of the pressure. This translates to: any money I save by not spending it on energy (where most of the money goes outside the country) can be spent on other things that might provide more local jobs. If enough of us do that we might delay the point of explosion by a little bit...and the longer we work on conservation and more efficient systems the greater the chance we have of coming out of a crash damaged and bruised but still alive. [At least give me time to get the money together to replace the oil heating I have in the property I have just bought...and to pay off more of the mortgage

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* Note: the down side is not likely to be a mirror image of the up side, but the image does depict the shape I want to describe. My guess is the down side will be more compressed than the up side.
** Note: One paper I read from an oil company, stated that energy efficency has been increasing by about 1% a year. This will "let off some of the steam", but with a world population increase of over that rate, it is clear that technological improvements have not let off enough steam, so pressure on energy resources is still building up.
We should teach our children the 4-Rs: Reduce, Reuse, Recycle and Rejoice.