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.