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Just a note

Notice that because this is a simple line plot, what looks like a curved line on the first graph is in fact a series of straight lines (interpolating between each pair of observations) - which, if you think about it, is not a very plausible model. However, because this is (in effect) a multiplicative model, when we use a logarithmic scale (as on the second graph) we obtain a simple linear relationship. This is because a constant proportion of the population are surviving to the end of each month.

However, if we 'de-transform' this simple linear relationship, we obtain a curvilinear interpolation between pairs of points - which is a much more plausible model.