What is the Exponential Function?

Have you ever thought, how do statisticians or mathematicians calculate the growth or decay of various viruses or usage of smartphones or depreciation of the economy?. All these things can be measured on the basis of growth or decay with the help of exponential function. It is the type of function in mathematics which helps to find the growth or decay of a particular observation or data. For example, a boy named: Jesse read an article about the growth of a virus, he read that every 2nd day the virus has exponential growth. You must note that an exponential function consists of a constant as the base and exponents as the variable, where ‘x’ is regarded as the variable and ‘a’ denotes the constant which should be smaller than Zero, ‘0’. In this article, we will try to cover some basic aspects of the exponential function such as the types of function and their differences. 

Exponential Growth Vs Exponential Decay 

The use of exponential function only arises when there is a growth or decay in a particular data or observation. There are two types of exponential function: exponential growth and exponential decay. As the name suggests, there must be some differences between them. The following points analyze the distinctive points between exponential growth and decay: 

  • You will observe that in exponential growth, the rate of quantity increases slowly and then reaches its gigantic height whereas, in an exponential decay, the data or observation decreases rapidly in the start and slows down till the end. For example, the covid virus increased in the month of February with the rate of 2 percent and suddenly with the rate of 15 percent in April; this is an example of exponential growth. 


  • Exponential growth is generally used to formulate or modulate the growth of population, the growth of compound interest annually, or the growth of some viruses. The exponential decay is basically used for modulating the decay or depreciation of population and economy, to find the value of half-life. 


  • As the name suggests, the graph of exponential growth function is always increasing whereas the graph of exponential decay function is always decreasing. 

Four Real-life Examples of Exponential Function 

 The type of function in mathematics which helps to find the growth or decay of a particular observation or data is known as an exponential function. The following points analyze those real-life examples:

  • The increase in the growth of microorganisms can be modulated with the help of exponential function.


  • The increase or decrease in the population of homo sapiens or human binges can be calculated with the help of exponential function. 


  • The rise in the cells of cancer in the human body can also be formulated by the help of this function. 


  • Have you heard about compound interest, it is the growth of interest annually. 

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