The Power of Exponentials, Big and Small

The Power of Exponentials, Big and Small


Swati Gupta, John Silberholz and Nataly Youssef
Operations Research Center
Massachusetts Institute of Technology
Cambridge, MA 02139, USA

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Exponential growth is keenly applicable to a variety of different fields ranging from cell growth in biology, nuclear chain reactions in physics to computational complexity in computer science. In this lesson, through various examples and activities, we have tried to compare exponential growth to polynomial growth and to develop an insight about how quickly the number can grow or decay in exponentials. A basic knowledge of scientific notation, plotting graphs and finding intersection of two functions is assumed. It would be better if the students have done pre-calculus, though this is not a requirement. The lesson is about 20 minutes, interspersed with simple activities that can require up to half an hour. We hope that all our viewers—teachers and students—enjoy watching the lecture and reflect on the magnitude of growth and decay of exponential functions.

Instructor Biography

Swati Gupta is a doctoral student at the Operations Research Center, MIT. She completed her bachelors and masters at IIT Delhi in Computer Science. Her research interests include algorithms, combinatorics and graph theory and she is currently working with Professors Michel Goemans and Patrick Jaillet.

John Silberholz is a doctoral student at the Operations Research Center, MIT. He completed his bachelors at the University of Maryland in Maths and Computer Science. He is currently researching large-scale optimization and healthcare analytics with Professor Dimitris Bertsimas.

Nataly Youssef is a doctoral student at the Operations Research Center, MIT. She completed her masters at Texas A&M University in Industrial and Systems Engineering and her bachelors at the Lebanese American University in Mechanical Engineering. She is currently working on applying robust optimization to stochastic analysis with Professor Dimitris Bertsimas.

Additional Online Resources

WNET School: Exploding Numbers
This site, presented by WNET School: The Practical Web Service for K-12 Teachers, provides a lesson that explores the concept of exponential growth, using two videos from WNET - one with Bill Nye the Science Guy and one from Math Talks.

Lesson Planet: Exponential Function
This resource, provided by Lesson Planet: The Search Engine for Teachers, includes teacher approved Exponential Function lesson plan ideas and activities.

Math Warehouse
This resource, provided by Math Warehouse, provides a simulation that allows students to observe the exponential growth of a bacteria colony.

Illuminations: Resources for Teaching Math
This site, Illuminations: Resources for Teaching Math, is sponsored by the National Council of Teachers of Mathematics and provides a Trout population calculator that allows students to observe how the actions of Wildlife Management affects the long-term population of trout in a pond.

Regents Exam Prep
This resource, sponsored by the Regents Exam Prep Center, provides 11 problems that give students practice with exponential equations and graphs.

This breaking news from IBM research shows that Moore's law should continue unabated for many more years. As we learn from this lesson, growing exponentials can grow very very fast.  Moore's Law says that the power of a computer chip will double roughly every 18 to 24 months.  This doubling of computer power has continued since 1958!  That's why today's smart phones have the computational power of multi-ton Cray super-computers of the 1970's.   But there was widespread worry that Moore's Law would stop operating in a few years.