Lesson 6B: Solving Exponential Equations
Alberta's Head-Smashed-In Buffalo Jump Interpretive Centre is part of a United Nations World Heritage Site. The deep layers of bison bones buried below the cliffs at this site represent about 6000 years of use of the buffalo jump by Aboriginal people of the Northern Plains. Using their excellent knowledge of the topography and of buffalo behaviour, they were able to kill their prey by chasing them over a precipice.
Archaeologists have studied artifacts and remains found at the Head-Smashed-In Buffalo Jump site. They believe the site was used as early as 3600 BCE. One of the tools archaeologists use to determine the age of an artifact made from plants or animals is carbon dating.
This procedure is based on the principle that plants and animals, while alive, utilize the various isotopes of carbon as basic building blocks. Carbon-14 is one of those isotopes. It decays at a constant rate and, when a plant or animal dies, the carbon-14 atoms that decay are not replaced. When the artifacts are examined in the laboratory, the remaining carbon-14 is measured and compared to what it would have been when the plant or animal was alive. The percentage of original carbon-14 that remains can be determined by solving an exponential equation.
An exponential equation is obtained from an exponential function—the unknown appears in the exponent. In this Training Camp, you will solve exponential equations and related problems.
By the end of this lesson, you should be able to
determine the solution of an exponential equation in which the bases are powers of one another determine the solution of an exponential equation in which the bases are not powers of one another