Growth Rate and Log Graphs
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Video Lecture 13 of 18
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### Lecture Description

It is good to know how fast different functions grow. Professor Strang puts them in order from slow to fast: logarithm of x, powers of x, exponential of x, x factorial, x to the x power; what is even faster?

And it is good to know how graphs can show the key numbers in the growth rate of a function. A log-log graph plots log y against log x. If y = A x^n then log y = log A + n log x = line with slope nA semilog graph plots log y against x If y = A 10^cx then log y = log A + cx = line with slope c. You will never see y = 0 on these graphs because log 0 is minus infinity. But n and c jump out clearly.

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The series is divided into three sections:
Introduction
- Why Professor Strang created these videos
- How to use the materials

Highlights of Calculus
- Five videos reviewing the key topics and ideas of calculus
- Applications to real-life situations and problems
- Additional summary slides and practice problems

Derivatives
- Twelve videos focused on differential calculus
- More applications to real-life situations and problems
- Additional summary slides and practice problems

Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.