## Growth Rate and Log Graphs

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 n

A 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.

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.