Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Compound Interest
Name: Steven
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
I am currently studying compounding interests. I have came across natural logarithms or the exponential 2.7182818.... .Now I do know that if ln x = y, 2.7182818^y=x but I have not yet understood what is so special about this number or what exactly is this number.... I mean why cannot we say that the e=2.6 or e 2.8? ;how has it been derived that e=2.7182818?



Replies:
The value of "e" is based on the slope of a graph. Mathmeticians wanted a function that had a slope at a point equal to the actual value of the original function at that point. Such a function has to be exponential, y=a^x for some base a. Each positive value of "a" yields a slope equal to the function value multiplied by a constant. To get slope and value perfectly equal, the base has to be 2.7182818.....

Kenneth Mellendorf



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory