Xkcd curve dating
Again, correct me if I'm wrong, but for the result of that, I get: I plotted that to find that the max was located at age t = 23. Integrating, you get -20(e^(-0.05(2x-14)) - e^(-0.05(x/2 7)))The derivative (eliminating the constant) is: (e^0.7)(-0.1)(e^(-0.1x)) (e^-0.35)(0.025)(e^(-0.025x))Wolfram gives about 32.5 as the root.
However, men are stupid, risk-taking fools whose bodies tend to degenerate faster, thus women tend to live, on average, six years longer than men.
The next step, then, would be to find the maximum area for any age.
To do this, we should be able to take the derivative of that previous equation, and set it equal to 0 in order to maximize it. The upper age limit is 2t-14 (as you note earlier in your comment) rather than the 2t 14 you mention later.
The dating range for any age, t, would be defined as: This agrees with the example in the XKCD strip.
The dating range for an 18 year old is from .5(18) 7 = 16 to 2(18)-14 = 22.
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(Thank Shakun, Marcott, Annan, Hadcrut and the IPCC for doing the tricky part.) First, guesstimate temperatures over last 20,000 years with anything at hand: tree-rings, ice bubbles, coral, fossilized tea leaves, whatever. Then stop the proxies, tack on thermometer data that was recorded in a different way with different errors and a very different response to faster temperature changes.