# which grows fastest?

• March 12th 2008, 08:22 PM
DINOCALC09
which grows fastest?
Which of the following functions grow faster then e^x as x approaches infinity?

x^4
ln(x)
e^(-x)
3^x
.5*e^x
• March 12th 2008, 08:38 PM
ThePerfectHacker
3^x because it is e^(xln 3) while e^x is just e^(x*1) and ln 3 > 1.
• March 13th 2008, 06:08 AM
colby2152
Quote:

Originally Posted by ThePerfectHacker
3^x because it is e^(xln 3) while e^x is just e^(x*1) and ln 3 > 1.

Another reason as to why...

$3^x > e^x$

Same exponent, but the left side has a larger base hence a larger outcome, and to connect this to TPH's explanation..

$ln|3|x > x$

$x \ne 0$ <- this follows because at zero the functions are equal

$ln|3| > 1$