23. The error connected with discrepancy of extrapolation exponential probability function by means of the linear

Probability function of destruction of a civilization - if to consider it process smooth in sense of probability, that is, of course, incorrect - it is possible to assimilate functions of disintegration of radioactive atom which, as is known, is described by exponent. For example, if the probability of  destruction of a civilization during the XXI century is equal 50 % as it is assumed by sir Martin Rees in the book «Our final hour» in 200 years, the chance of the survival of the civilization will be 25 %, and through one thousand years - only 0.1 % - at uniform preservation of the same tendencies. From here it is visible, that it is incorrect to conclude, that if chances of the survival within a millennium makes 0.1 % for one century it will be in only ten times more, that is 1 %. The same error in less obvious kind arises, if we need to extrapolate the same 50 % of a survival within 100 years on annual probability of  destruction. Linear approximation would give 0.5 % for a year. However the exact value calculated under formula , makes approximately 0,7 %, that is in 1,4 times above, than intuitive linear approximation gives.