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Math students learn to see how two amounts relate to each other. A function links two things. It uses a rule to show how one item from a set of inputs matches just one item from a set of outputs. An exponential function follows a pattern, where a is a number that is always positive but is not 1.

Don’t mix exponential functions with polynomial functions.

The name of the function is one way to tell the two functions apart. Exponential functions are named this way because the variable is in the exponent of the function. These functions are often recognized by the fact that their rate of growth is proportional to their value.

This idea of exponential growth has been around for a long time, even before calculus was invented.

Figuring out the exponential function gives a good result for the exponential function’s series expansion with negative powers. It’s not just that computers and programs like MATLAB sometimes get the math wrong for negative powers. The main problem is that many important calculations still use this expansion with negative powers in a way that is incorrect. This expansion is important for negative powers. 

Exponential function in our real-life

Exponential functions show growth or decline in the world when change happens at varying speeds. We see this with populations and investments growing, radioactive things breaking down, and online content spreading. They also let us track when diseases spread, see how much medicine someone has taken, and calculate interest that grows.

Exponential Growth

These are circumstances where a number rises at an hurrying rate. 

Population Growth: 

The number of people or organisms in a population can grow exponentially, especially under satisfactory conditions.  One of the vital functions of the demographers is to offer information on the upcoming fashion of population forecast, which is vital to plan for human events. Nowadays, demographers are attentive in telling phenomena in theoretical models involving population structure by seeing the stochastic similarities of standard changes and differential equations. A explanation of a population forecast model is resulting using a growing rate follow a birth and death diffusion process. The mean and the variance as well as the forecast and the virtual sample path of such a population forecast progression are also got. Mathematical illustration for the case of the birth and death flow development rate as well as the case of the continuous growth rate are reflected.

Compound Interest: 

Money in an investment can raise exponentially as the interest made also begins to make interest, principal to quicker progress over time.  Real long-term deal wants a well-structured strategy supported by comprehensive examination. The compound interest model helps as an essential device in evaluating potential yields on investments by exemplifying how interest accumulates on both the first wealth and before grown interest. A researcher investigates addicted to the request of compound interest in investment collections, pointing to explain its impression on long-standing growing trajectories. By exploring numerous causes, such as investment length and compounding occurrence, the investigation best part the complicated tools dynamic deal expansion. A healthy understanding of these fundamentals is vital aimed at creating knowledgeable financial conclusions.

The study’s ideas will help people involved and business advisors with practical plans to make better choices. This will lead to better investment results, which will help create more long-lasting investments.

Exponential Functions in Real Life: Conclusion

Exponential functions are very important for understanding how things grow and shrink in real life. They give us powerful ways to show changes in populations, interest on money, medicine, and technology. If people know what makes them special, we can study real problems and make good decisions in real life.  

FAQs

Q1: How do we use exponential functions in real life?

A: Examples of exponential functions in real life include bacteria growth and compound interest. An example of exponential decay in is how quickly radioactive materials break down.

Additionally, to stay updated with the latest developments in STEM research, visit ENTECH Online. Basically, this is our digital magazine for science, technology, engineering, and mathematics. Further, at ENTECH Online, you’ll find a wealth of information.

References

1. Janardana, K., & Wiriandi, D. I. (2024). The Application of Compound Interest in Investment Portfolios. International Journal of Quantitative Research and Modeling, 5(4), 427–431. https://doi.org/10.46336/ijqrm.v5i4.829