### Abstract:

The rate of atmospheric formation of radiocarbon (C-14) was long considered to be relatively constant over time during the Holocene and late Pleistocene epoch. Because living tissue fixes carbon derived from the atmosphere, the result is a fairly constant proportion of radioactive C-14 to stable C-12 in living plants and animals. Using the measured half-life of C-14 (5,730 years), the approximate age of plant and animal tissue containing C-14 extending back as far as 30,000 ybp can be calculated. However, the C-14 dating technique is not as accurate as was once believed because it has been discovered that the ratio of C-14 to C-12 in the atmosphere fluctuates with time.In an attempt to determine the degree of fluctuation in the C-14 to C-12 ratio, scientists have attempted to calibrate C-14 ages with the more reliable dendrochronological ages. Since a dendrochronological time scale has been verified by Becker (1993) for the last 11,000 ybp, the degree of fluctuation in the rate of C-14 production during the past 11,000 ybp is known. This has resulted in the compilation of C-14 calibration curves which reveal the presence of both a long-term and several short-term deviations in the C-14 to C-12 ratio of the atmosphere over the past 11,000 ybp. The difficulty scientists are still currently faced with, however, is how to interpret C-14 ages in the range of 11,000 to 30,000 ybp, beyond the dendrochronological time scale but within the present limit of C-14 dating methods. In an attempt to solve the dilemma of how to interpret C-14 ages in this age range, this paper offers: 1. A detailed summary of the dendrochronological, C-14 dating, and C-14 calibration via dendrochronological analysis methods; and 2. A complete extrapolation of an existing C-14 calibration curve out to 30,000 ybp.Using an extrapolation of both a best-fit straight line trend and a periodic oscillating trend (each with a C-14 deviation of + 100 C-14 years), a method of calibration for C-14 dates greater than 11,000 ybp is created by using both trends in conjunction with one another (Figure 3). This method, when applied to the existing calibration curve in Figure 1, shows a maximum increase in deviation of 335 dendrochronological years in addition to the 265 years produced at a C-14 age of 4,700 yr by by conventional analysis. In the range of extrapolation from 11,000 to 30,000 ybp, a maximum age difference between a best-fit straight line trend and periodic oscillating trend of ± 688 actual cal (calibrated) years is present at an approximate C-14 age of 23,000 yr by (Figure 2). At 30,000 years cal BP the two trends, however, differ by only ± 425 actual cal years which corresponds to a C-14 age of 26,500 yr bp. The 3,500 year difference between C-14 and dendrochronological age scales at 30,000 years cal BP results in part from the long and short-term deviations previously mentioned, and in part from a 3% short fall in using the Libby half-life (5,568 years used by Stuiver and Becker (1993) to make the calibration curve used in Figure 1 of this paper) instead of the more recently determined and more accurate half-life of 5,730 years.This method of extrapolation is in close accordance with the U-Th dating method used by Bard et. al. (1990). The maximum difference of approximately 3,500 years between C-14 and dendrochronological dates at 30,000 ybp equals the approximate 3,500 year maximum difference found between C-14 and U-Th ages at 20,000 ybp by Bard et. al. (1990). In addition, this correlation holds true even though these authors used the more accurate 5,730 year half-life in their extrapolation of C-14 instead of the Libby half-life used in Figure 1 of this paper. Therefore, the method of extrapolation presented here could be used as a reasonable first order check of approximate calendric age ranges for respective C-14 ages. This method of extrapolation would also be useful for checking the reasonableness of other C-14 calibration techniques in the range of 11,000 to 30,000 ybp. This analysis of extrapolating the calibration curve indicates that continued work on measuring the ratio of C-14 to dendrochronologically derived ages in materials older than 11,000 ybp is justified.