f(x)=-72 +73.6 ln x

Question

About 80% of finnish workers are members of a trade union. The number of labor disputes in Finland from 2000 to 2011 can be modeled by

 f(x) = -72 + 73.6 ln x       10 <=  x <=21

 where x represents the number of years since 1990, and f(x) represents the number of labor disputes  annually. Determine the average  value of  f  on the interval  [11,21] and interpret.

Answer 1

The table shows the figures between 2001 and 2011, where x in [11,21]. The figures in the rounded column represent the whole numbers of disputes in the year as predicted by the model. As it happens the average of these matches closely the average of the model’s predictions, at 131. The rise in the number of disputes is almost linear, with 4 or 5 additional disputes occurring with each additional year. The average occurs around the centre of the range of years. The average of the first and last years is (104+152)/2=128. This figure, too, is roughly central. The median is 132, slightly higher than the mean (average).