Carbon-14 is an isotope of carbon that is formed when radiation from the sun strikes ordinary carbon dioxide in the atmosphere. Trees, which get their carbon dioxide from the air, contain small amounts of carbon-14. Once a tree is cut down, no more carbon-14 is formed, and the amount that is present begins to decay slowly. The half-life of the carbon-14 isotope is 5730 yr.
a. Find an equation that models the percentage of carbon-14 in a sample of wood. (Consider that at time zero there is 100% and that at time 5730 yr there is 50%.)
b. A piece of wood contains 48.37% of its original carbon-14. According to this information, approximately how long ago did the tree that it came from die? What assumptions are you making, and why is this answer approximate?