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It is often believed that the mortality intensity in the modern human population undergoes an exponential growth after 40 years, i.e. the actuarial aging rate is regarded to be constant after 40 years. To check this assumption we have calculated local aging rate values for 13 age ranges (within the interval of 30-92 years) for the male and female population of 48 states of the US (1969-1971). It was found that generally the male aging rate is not constant but lowers monotonically with time, while for females the aging rate has a pronounced approximately-shaped character with a minimum in the range of 45-60 years and a maximum within the range of 70-80 years. The results obtained are a warning to those who boldly use Gompertz or Gompertz-Makeham formulas when describing human aging on the population level.