# Is f(x)=x^2 an exponential function?

May 28, 2015

Well, no...this is power called a quadratic.
There is a slight but very important difference between the power and the exponential that concerns the "position" of $x$;
Power: the $x$ is...at the ground floor and the number, say $a$, in the attic!
${x}^{a}$
Exponential: the other way round; now $x$ is in the attic and the number at the ground floor:
${a}^{x}$
Seems trivial but have a look:
$y = {x}^{2}$
graph{x^2 [-10, 10, -5, 5]}

$y = {2}^{x}$
graph{2^x [-11.39, 11.11, -2.61, 8.64]}

And compare values:

Would you like your salary be modelled by a quadratic or exponential??? :-)