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.

November 4, in Real life maths , statistics Tags: probability density function , radioactive decay. We can now use this to solve problems involving Carbon which is used in Carbon-dating techniques to find out how old things are. How old is this paper? We can then manipulate this into the form of a probability density function — by finding the constant a which makes the area underneath the curve equal to 1.

One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. In this section, we examine exponential growth and decay in the context of some of these applications. Many systems exhibit exponential growth. Notice that in an exponential growth model, we have.

The first example deals with radiocarbon dating. The concept is kind of simple:. Every living being exchanges the chemical element carbon during its entire live.

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