Title
Outbreak: A Deadly Virus (October Crowell)
Goals
(1) Students will investigate exponential growth through a futuristic problem situation
(2) Students will derive a closed form recursion equation based on the data.
Abstract
This activity is designed to allow students to investigate recursion theory and geometric sequences through a hypothetical model. It should be used in conjunction with study on sequences and recursion.
Problem Statement
Recently, with the outbreak of the e-coli virus, scientists have been concerned that a more powerful deadly virus could wipe out the entire species of humans in a short period of time. To find out how quick this could happen, we will investigate the spread of such a virus and exactly how long we would survive in such a situation.
Instructor Suggestions
(1) Introduce the problem
(2) Have students work in small groups to find the solutions and equation.
(3) Discuss as a whole class the results and the implications of the results.
*This activity could also be done individually and discussed in class at a later date.
Materials
"Outbreak: A Deadly Virus" activity sheet
Time
Introduction (5 min), Group work (20 min), Class discussion (15 min)
Mathematics Concepts
Discrete Mathematics Concepts
Recursion, Geometric sequences
Related Mathematics Concepts
geometric sequences, exponential growth
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Functions, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5)
Curriculum Integration
This activity could be integrated into an Advanced Algebra or Pre-Calculus class when the topic of sequences and recursion is introduced.
Further Investigation
Students could further investigate rates of human extinction with different degrees of rate of spread of the virus.
Variations/Comments
References/Resources
Colorado State Content Standards. Colorado Department of Education.
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics across the curriculum, K-12, Reston, VA; National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics, (1989). Curriculum and evaluation standards for school mathematics. Reston, VA; Author.
http://www.census.gov/main/www/popclock.html (for current population counts)