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

Question

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.

Answer 1

It means $\large y=Ae^{6x}$

The function $e^x$ is often denoted with exp(x).

Answer 2

$\exp$ 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.

Answer 3

$\exp(x)$ 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 $\exp(\frac{e^x}{x^2+x+1}+1)$