# PBL Pathways

##### Content Area

College Algebra, Precalculus

2 to 3 weeks

December 4, 2009

##### Keywords

Exponential decay, exponential equations

#### Project Title

Potassium-Argon Dating

#### Author

David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

#### Abstract

This contrived project helps students to understand the various methods used to date artifacts and rocks. In this project, each students is given the half-life of Potassium 40 and the amount of Potassium 40 and Argon 40 in a sample (every student gets an amount based on the number of letters in their name). Using this information, they find the age of the sample.

#### Project Content

Project Letter DOC | PDF

#### Scaffolding Resources

Technology Assignment: Exponential Equations DOC | PDF | VIDEO - This technology helps students to solve an exponential equation using the Method of Intersection in Excel.

Handout DOC | PDF - This document explains how Carbon 14 dating works and can act as a template for the project.

#### Notes

• I have used this project several times. The toughest part for most students is finding the initial amount. They have a hard time seeing how Potassium 40 gradually changes to Argon 40. The C14 handout was designed to help remedy this problem.
• The concept of finding the constants y0 and k is also tough. Most students can get through finding the constants with a bit of work, but then struggle with using the resulting equation to find the age of the rock sample.
• I require students to solve for the age algebraically, and then to verify the solution graphically. The best students verify that the model equation is correct by checking the the half-life AND verify the age using the Method of Intersection.
• Students will often ask how much they should round the constants. Have them experiment with rounding to different decimal places to see the effect on the age.