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When Does $0 of Value Occur?

An old issue of the U.S. News & World report assumes that the one dollar bill in 1945 was worth 100 cents. Then, the journal reveals the relative purchasing power of that dollar bill in future years:

  • Year 1953--67 cents
  • Year 1961--60 cents
  • Year 1963--58 cents
  • Year 1969--50 cents
  • Year 1974--36 cents
  • Year 1977--30 cents
  • Year 1979--24 cents
Question: Based on this data, when will the one dollar bill have a purchasing power of 1 cent? 0 cents?

Note: Is it linear, exponential,...or?

Also, why are these predictive situation troublesome?