# What Does $y=A\exp(6x)$ mean?

So my professor used this and I don't really know what this equation means. $A$ is a positive constant, different $A$'s give different curves and these curves form a family $\mathcal{F}$. Given a point, let $C$ be the member of the family that goes through this point. Find the equation of $C$ as $y=f(x)$.

I purposely left out the point because I want to do the question myself and posted the whole question as background information, but what does the $\exp$ part mean? Thanks.

Note: I googled this extensively and couldn't find an answer, looked here too.

• I feel like a big noob thanks
– Jeff
Commented Jan 18, 2015 at 21:35
• If your professor used it and you don't know what it is, you should ask him. Maybe he inadvertently used something too advanced for the class. Or maybe the rest of the class knows it and you need some catching up. Or even a more elementary class. Commented Jan 18, 2015 at 21:50
• To add to the answers below, sometimes it is easier to see Chain Rules when we write $\exp(f(x))$ rather than $e^{f(x)}$. Commented Jan 18, 2015 at 21:53
• @GEdgar: I think George knows what $e^x$ is but just didn't know that it could be written as $\operatorname{exp}(x).$ Commented Jan 18, 2015 at 21:54
• Mathematicians say exp(x), EECS types say $e^{x}$. The first time any of us saw it it felt weird.
– smci
Commented Jan 18, 2015 at 23:57

It means $\large y=Ae^{6x}$
The function $e^x$ is often denoted with exp(x).
$\exp$ is the Exponential function.
The notation $\exp(x) = e^x$ is also common, because it can be evaluated as the number $e \approx 2.71$ raised to power $x$.
Some properties of $\exp$ are for example that the $n$th derivative of $\exp$ is itself, as well as it's $n$th antiderivative.
$\exp(x)$ is simply, as others have said, $e^x$. This is used when it's awkward to make the thing being exponentiated smaller and offset, such as $e^{\frac{e^x}{x^2+x+1}+1}$ which would be written instead as $\exp(\frac{e^x}{x^2+x+1}+1)$