Question

Is the function ƒ(x) = e–11x an exponential function? If so, identify the base. If not, why not?

Answer 1

Answer:

Yes

$y=e^{-11x}=\frac{1}{e^{11x}}=\frac{1}{e^{11}} \frac{1}{e^x}=\frac{1}{e^{11}} e^{-x}$

So then we see that the base on this case is: $c=\frac{1}{e^{11}}$ , so then our function can be considered as an exponential function.

Step-by-step explanation:

First we need to define an exponential function.

The exponential function with a base c is givn by the following expression:

$f(x)=c^x$, and $c>0, c\neq 1$ and x can be any real number.

The exponential function have always a base and a variable. The value c it's called the base and x the variable.

The exponential function is defined as:

$y=e^x$

And the function given by:

$y=\frac{1}{e^x}$ is called the natural exponential function.

For our special case our function is given by:

$y=e^{-11x}=\frac{1}{e^{11x}}=\frac{1}{e^{11}} \frac{1}{e^x}=\frac{1}{e^{11}} e^{-x}$

So then we see that the base on this case is: $c=\frac{1}{e^{11}}$ , so then our function can be considered as an exponential function.