Carbon-14 Dating Problem: The ages of things, such as wood, bone, and cloth, that are

Chapter 7, Problem 3

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Carbon-14 Dating Problem: The ages of things, such as wood, bone, and cloth, that are made from materials that had been living can be determined by measuring the percentage of the original radioactive carbon-14 that remains in them. This table contains data on the age as a function of the remaining percentage of carbon-14. Percentage Years Remaining Old 100 0 90 874 80 1851 70 2959 60 4238 50 5750 The skull of the saber-toothed cat, which lived in the Pleistocene more than 11,000 years ago. a. Based on theoretical considerations, it is known that the percentage of carbon-14 remaining is an exponential function of the age. How does this fact indicate that the age should be a logarithmic function of percentage? b. Using the first and last points, find the particular equation of the logarithmic function that goes through the points. Show that the equation gives values for other points close to the ones in the table. c. You can use your mathematical model to interpolate between the given data points to find fairly precise ages. Suppose that a piece of human bone were found to have a carbon-14 content of 73.9%. What would you predict its age to be? d. How old would you predict a piece of wood to be if its carbon-14 content were only 20%? resource to find out about early hominid fossil remains and carbon-14 dating.