I think that we can easily survive and get off this planet / out of this solar system in due time, however it's not going to be because of exponential growth. If anything, exponential growth is what's going to kill us all. We're using resources way faster than they can be replenished or replaced, and exponential growth is only going to make it worse.
Everyone know of the doubling time? 70/x, where x is the percent growth / time unit. So if the growth rate was 10% / year, the doubling time would be 7 years. The earth has about 45 million square miles of dry land, Antartica excluded (about 116 quadrillion square meters - or 1.16*10^14 sq m). The current world population is about 6.5 billion (6.5*10^9) people, and the growth rate is about 1.5 percent, leaving the doubling time at about 47 years. Now you can do the calculations if you care to... It would take a little over 14 doubling times for the population of the earth to reach the area of the dry landmass in square meters. So in some 660 years, the population density over the entire earth will have reached one person per square meter.
This obviously assumes that the population growth does not slow over time, which it should. The rate of population growth in developed countries is way less than that in undeveloped countries, so much so that while undeveloped countries can easily double their population in 40 years, the population in developed countries has plateaued. This is a good thing, for as the "undeveloped" countries become "developed", the population growth will actually stop, which should somewhat lighten our load on the enviornment.
However, industrial growth remains a problem, and seems to maintain this exponential growth despite decrease in populaiton growth, thanks largely, I would imagine, to automation. Conventional oil supplies, with the current use and rate of growth (2%), will deplete the words oil reserves before 2050. Granted, this does not take into account the sources of "nonconventional" oil (tar deposits, are one that I know of) which are basically anything that has a similar hydrocarbon structure to oil, however no one is using this nonconventional oil because no one knows how to drill for it or process it yet. Oh, did I mention that the oil output is predicted to peak within 2 years?
So, yeah... I think we can make it. I don't think death is imminent, but we sure as hell have to keep ourselves in check.
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C4 to your door, no beef no more...
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