# Examples of exponential growth and decay in real life

## Exponential Growth in real world

Exponential Growth and Decay - Real Life Application

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In real-world applications, we need to model the behavior of a function. In mathematical modeling, we choose a familiar general function with properties that suggest that it will model the real-world phenomenon we wish to analyze. In the case of rapid growth, we may choose the exponential growth function:. We may use the exponential growth function in applications involving doubling time , the time it takes for a quantity to double. Such phenomena as wildlife populations, financial investments, biological samples, and natural resources may exhibit growth based on a doubling time. In some applications, however, as we will see when we discuss the logistic equation, the logistic model sometimes fits the data better than the exponential model. On the other hand, if a quantity is falling rapidly toward zero, without ever reaching zero, then we should probably choose the exponential decay model.

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Exponents, Index Numbers, Powers, and Indices are used in lots of parts of our modern technological world. Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas. In this lesson we show several Real Life uses of Exponents, as well as their impact on our understanding of the modern world around us. Exponents are fundamental, especially in Base 2 and Base 16, as well as in Physics and Electronics formulas involved in Computing. There has been an Exponential increase in the speed and power of computers over recent years, and by around computing power is predicted to match that of the human brain.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Next lesson. Current timeTotal duration Exponential growth and decay Modeling with exponential functions. Video transcript Let's do a couple of word problems dealing with exponential growth and decay. So this first problem, suppose a radioactive substance decays at a rate of 3.

## Exponents in the Real World

One of the "home grown" examples is a gradual diminishing of a temperature of a hot body down to room temperature. For instance, the kettle with boiling water cools down after the heater is turned off. The physical law describing this process of cooling sounds like this: The speed of a cooling of a hot object is proportional to a difference in temperature between the cooling body and environment, assuming that the environment is large enough to absorb the heat without really changing its own temperature.

## Exponential growth & decay word problems

In mathematics, exponential decay occurs when an original amount is reduced by a consistent rate or percentage of the total over a period of time, and the purpose of this concept is to use the exponential decay function to make predictions about market trends and expectations for impending losses. The exponential decay function can be expressed by the following formula:. But how often does one find a real world application for this formula? Well, people who work in the fields of finance, science, marketing, and even politics use exponential decay to observe downward trends in markets, sales, populations, and even poll results. Restaurant owners, goods manufacturers and traders, market researchers, stock salesmen, data analysts, engineers, biology researchers, teachers, mathematicians, accountants, sales representatives, political campaign managers and advisors, and even small business owners rely on the exponential decay formula to inform their investment and loan-taking decisions. However, too much of a good thing can be detrimental, especially when it comes to natural resources like salt.

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## Exponential Growth and Decay Real World Applications.

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Exponential growth & decay word problems (video) | Khan Academy