# Exponential growth and decay in the real world project

## World Population Project (Algebra 1 Exponential Functions Resources)

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Exponential growth and decay are the two functions to determine the growth and decay in a stated pattern. Exponential growth and decay formula can be used in a particular situation if a quantity grows at regular intervals, the pattern of the function can be depicted and summarised in an algebraic equation. The population of a hometown in Scotland in was estimated to be 35, in that year. The population is expected to grow with an annual increase of 2. What is the growth factor of home town in Scotland and use the estimate to calculate the population of the hometown for the next 4 years?

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. Compound Interest also works against people with a Credit Card debt they do not pay off, because the debt grows faster and faster each billing period and can quickly become out of control. Over the last few years there has been massive exponential increases in mobile phone usage and market penetration.

The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. We will discuss in this lesson three of the most common applications: population growth , exponential decay , and compound interest. For other applications, consult your textbook or ask your teacher for additional examples. Population Many times scientists will start with a certain number of bacteria or animals and watch how the population grows. For example, if the population doubles every 5 days, this can be represented as an exponential function. Most population models involve using the number e.

## Exponential Growth in real world

Exponential Growth & Decay Examples

## Exponential & logistic growth

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My students recently took their end of unit test over exponential functions writing them and graphing them …and it was a disaster. They all went into a panic during the test, and their results were about as bad as they feared they would be. I clearly had not prepared them well enough. I went into a panic of my own, decided that I could not put that test in the gradebook, went back to the drawing board, and came up with some review activities for us to do over the next few days. I also decided that engaging with real data in a way that would be pretty difficult would potentially prepare them to engage with the more sanitized numbers and scenarios of test problems more confidently. I employ this strategy frequently — putting problems in notes or practice that are more complex than any that will be on their tests, so that then the tests seem easy in comparison. Many of our example problems involved populations, so my brain came up with world populations!

We have already explored some basic applications of exponential and logarithmic functions. 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.

To a mathematician, however, the term exponential growth has a very specific meaning. In this section, we will take a look at exponential functions , which model this kind of rapid growth.

## Exponential Functions Applications

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. As a result, a lawmaker once introduced legislation that would force Americans to cut back on their consumption of salt.

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