The **exponential function** is the opposite of that of the neperian logarithm and is mathematically denoted by the formula *f*(*x*)=e^{x}. With this premise in mind, the exponential function is used in many mathematical problems.

With our **exponential function calculator**you will be able to calculate this operation involving Euler's number.

Article sections

## Properties of the exponential function

The exponential function has a series of** rules we must know** and which are detailed below:

- exp (x + y) = exp(x) - exp(y)
- exp (x - y) = exp(x) / exp(y)
- exp (-x) = 1/exp(x)
- exp (0) = 1

Taking into account these **four properties for exponential functions**If you have to use the calculator, you will be able to greatly simplify your calculations when you encounter derivatives, integrals or other mathematical operations where they are present.

## Exponential growth What does it mean?

For a good understanding **what does exponential growth mean** we thought it convenient to accompany the explanation of the graph of the function e^{x} for the sake of clarity.

If you notice, for negative lower values of the exponential function, the value of y hardly increases. However, for positive values of x, **the growth of y shoots up to tend to infinity**.

Another thing you can appreciate about the exponential function is that **will never result in a negative number.**Therefore, its range is from zero to infinity and, therefore, it is an increasing function.

## Derivative of the exponential function

The derivative of an exponential function results in the exponential function itself.

## Integral of the exponential function

If we take into account that the integral is considered as the antiderivative, then we can already have a clue as to what the integral of the exponentials will be.

As is the case with derivatives, the integral of an exponential function is the function itself plus the constant C.

## Value of Euler number

As we have already mentioned, exponential functions are characterized by the fact that the **number e** or Euler number is involved, but what is its value?

Number e = 2.71828182....

The number e **has infinite decimal numbers** since it is a rational number, exactly the same as the PI number so in order to work with Euler's number, it is best to take a number of three or four decimal places to add more than enough precision for school or university exercises.

## How to calculate an exponential in Excel

It is clear that Excel is also another tool for **calculate the value of an exponential**. To do this you must make use of this formula:

=EXP()

and in parentheses write the value of the exponent that is applied on the base e.

## EXP on scientific calculator

In the case of scientific calculators, it depends a bit on the model you have. In the case of many Scientific Casio you will have to **locate the 'ln' key since its secondary function will be the one we will be using** to calculate an exponential.

For example, if we want to calculate e^{4}If you want to change the keystroke, you must press the following combination of keys:

SHIFT → LN → 4 → ) → =

We have used the parenthesis because the model of scientific calculator we are using opens one when we press the button to calculate exponentials so we have to close it so that when we press the equals key the operation does not give us an error.

If you have any remaining questions about how to solve a power with the **base Euler number**Please leave us a comment and we will try to answer you as soon as possible to help you.