extrapolation vs reasoning

extrapolation

noun
  • An inference about some hypothetical situation based on known facts. 

  • A calculation of an estimate of the value of some function outside the range of known values. 

  • The diametric opposite of interpolation. 

reasoning

noun
  • The deduction of inferences or interpretations from premises, abstract thought, ratiocination; (countable) any instance of this, especially as a process leading to an action, motive. 

  • A Rastafari meeting held for the purposes of chanting, prayer and discussion. 

How often have the words extrapolation and reasoning occurred in a corpus of books? (source: Google Ngram Viewer )