What is an Exponential Function?


In mathematics, a function that is used to measure the growth also called the exponential growth, or to modulate the ups and downs of the population is defined as the exponential function. For example, You may read an article representing the growth of coronavirus. The virus was mild and spread with a rate of 5 percent in the first week, in the second week the virus got severe and it got spread with a rate of 10 percent. This article is expressed and represented exponentially. In this article, we will try to cover some basic concepts regarding exponential function such as the comparison between exponential growth and decay, some real-life examples of the exponential function, and do a detailed analysis about them.

Differences Between Exponential Growth and Exponential Decay

In the paragraph mentioned above, we dealt with the definition of exponential function and covered a basic overview of it. We will try to cover some differences between the growth and decay of any chart exponentially. The following points analyses the distinctive features between them.

  • You will observe that in an exponential growth the number increases slowly but changes with a huge number till the end whereas in an exponential decay the number decreases very fast in the initial point but slows down till the terminal point.

  • The uses of exponential growth are as follows, to compute the population change, modulate the compound interest, double time, etc. The uses of exponential decay are as follows, to calculate the half-life, population decay, etc.

  • Whenever you observe a bar graph or a coordinate graph of exponential growth, you will see that the graph always increases whereas on the contrary the graph of exponential decay always decreases.

Some Real-Life Examples of Exponential Function

Till now, you may have understood the concept of exponential function and different types of it such as exponential growth and decay. Let us now deal with the real-life examples of this type of function. The points mentioned below signify the examples in real life.

  • Population of Homo Sapiens: Nowadays, the population of human beings has been increasing exponentially. As of now,  China is the largest populated country but it is assumed that India may be the highest populated country till 2030.

  • Have you heard about the term compound interest, it is the addition of the value of interest to the deposit or loan. The constant interest rate gives exponential growth to the capital mentioned.

  • Examples of exponential growth are seen everywhere such as the growth of cancer cells, the spreading of a virus, the microorganism present in an object, or the growth of mold in bread. All these things are examples of exponential growth.

Exponential Function Vs Linear Function

The following points analyze the comparison between exponential and linear functions.

A function that is used to measure the growth also called the exponential growth or to modulate the ups and downs of the population is defined as the exponential function whereas the linear function is a type of function consisting of two variables with no exponents.

In a bar graph the linear function forms a straight line whereas in an exponential function the line which is formed is curved.

The linear function will always have a growth of zero whereas the exponential function will never have a growth of zero.

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