# What is exponential function?

## What Does exponential function Mean

In order to know the meaning of the term exponential function that concerns us now, it is necessary first to discover the etymological origin of the two words that give it its shape:

-Function, first of all, it derives from Latin, exactly from "functio", which can be translated as "exercise" or "function". Likewise, that comes from the verb “fungi”, which is synonymous with “fulfill” or “perform a task”.

-Exponential, secondly, it also derives from Latin. It means “growth that increases more and more rapidly” and is the result of the sum of several lexical components of that language: the prefix “ex-”, which is synonymous with “outwards”; the verb “put”, which can be translated as “put”; the particle "-nt-", which is used to indicate agent, and the suffix "-al", which means "relative to."

In the realm of mathematics , a function is a link between two sets whereby each element of the first set is assigned a single element of the second set or none at all. Exponential , on the other hand, is an adjective that describes the type of growth whose rate is increasing faster and faster.

According to its characteristics, there are different types of mathematical functions . An exponential function is a function that is represented by the equation f (x) = aˣ , in which the independent variable ( x ) is an exponent.
An exponential function, therefore, makes it possible to refer to phenomena that grow faster and faster . Take the case of the development of a bacterial population: a certain species of bacteria that, every hour, triples its number of members. This means that every x hours there will be 3ˣ bacteria .
The exponential function indicates that, starting from a bacterium:
After one hour: f (1) = 3¹ = 3 (there will be three bacteria)

After two hours: f (2) = 3² = 9 (there will be nine bacteria)

After three hours: f (3) = 3³ = 27 ( there will be twenty-seven bacteria)

Etc.
Returning to the equation f (x) = aˣ , it must be taken into account that a is the base , while x is the exponent. In the case of the example of bacteria that triples every hour, the base is 3 , while the exponent is the independent variable that changes over time.
In exponential functions, the set of real numbers constitutes their domain of definition. The function itself, on the other hand, is its derivative .
In addition to all the above, we cannot ignore another series of relevant data on the exponential function such as the following:

-It is of continuous class.

-It is determined that it is increasing if a> 1 and that it is decreasing if a <1. -Exponential functions can be used in a wide variety of sectors to carry out endless calculations. However, they are used in a forceful way when working with population growth in a specific area, in terms of compound interest in terms of the economic issue and also to work with the so-called radioactive decay.

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