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.

## Light attenuation and exponential laws

## Fluorescence intensity decay models - The fluorescence laboratory.

A double exponential function is a constant raised to the power of an exponential function. Factorials grow more quickly than exponential functions, but much more slowly than doubly exponential functions. However, tetration and the Ackermann function grow faster. See Big O notation for a comparison of the rate of growth of various functions. The inverse of the double exponential function is the double logarithm ln ln x. Aho and Sloane observed that in several important integer sequences , each term is a constant plus the square of the previous term.

### Exponential Growth and Decay

Search this site. DecayFit - Fluorescence Decay Analysis. AniFit - Anisotropy Decay Analysis. DecayFit Documentation Pages. AniFit Documentation Pages.

If you missed this problem, review here and scroll to Example 4. Note that this will open a different textbook in a new window. If you missed this problem, review here. If you missed this problem, review Section 1.

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