question: What calculation uses 8,033, the mean-life derived from Libby's half-life of 5,568 years?
context: The calculations to be performed on the measurements taken depend on the technology used, since beta counters measure the sample's radioactivity whereas AMS determines the ratio of the three different carbon isotopes in the sample.To determine the age of a sample whose activity has been measured by beta counting, the ratio of its activity to the activity of the standard must be found. To determine this, a blank sample (of old, or dead, carbon) is measured, and a sample of known activity is measured. The additional samples allow errors such as background radiation and systematic errors in the laboratory setup to be detected and corrected for. The most common standard sample material is oxalic acid, such as the HOxII standard, 1,000 lb of which was prepared by the National Institute of Standards and Technology (NIST) in 1977 from French beet harvests.The results from AMS testing are in the form of ratios of 12C, 13C, and 14C, which are used to calculate Fm, the "fraction modern". This is defined as the ratio between the 14C/12C ratio in the sample and the 14C/12C ratio in modern carbon, which is in turn defined as the 14C/12C ratio that would have been measured in 1950 had there been no fossil fuel effect.Both beta counting and AMS results have to be corrected for fractionation. This is necessary because different materials of the same age, which because of fractionation have naturally different 14C/12C ratios, will appear to be of different ages because the 14C/12C ratio is taken as the indicator of age. To avoid this, all radiocarbon measurements are converted to the measurement that would have been seen had the sample been made of wood, which has a known δ13C value of −25‰.Once the corrected 14C/12C ratio is known, a "radiocarbon age" is calculated using:
    
      
        
          
            Age
          
          =
          −
          8033
          ⋅
          ln
          ⁡
          (
          F
          m
          )
        
      
      {\displaystyle {\text{Age}}=-8033\cdot \ln(Fm)}
    The calculation uses 8,033, the mean-life derived from Libby's half-life of 5,568 years, not 8,267, the mean-life derived from the more accurate modern value of 5,730 years. Libby’s value for the half-life is used to maintain consistency with early radiocarbon testing results; calibration curves include a correction for this, so the accuracy of final reported calendar ages is assured.
answers.text: radiocarbon age