As you learn about modelling exponential growth and decay, recall familiar techniques that have helped you to model situations using other types of functions. The exponential growth and decay models possess input and corresponding output like other functions graphed in the real plane. They also adhere to the characteristic feature of the graphs of all functions; each point corresponding input and output pairs contained on the graph of the function satisfies the equation of the function. You can rely on these features as you work with the form of the function to fill in known quantities from a given situation to solve for unknowns. 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.

## Exponential Growth and Decay

## BioMath: Carbon Dating

This section begins with a discussion of exponential growth and decay, which you have probably already seen in calculus. We consider applications to radioactive decay, carbon dating, and compound interest. We also consider more complicated problems where the rate of change of a quantity is in part proportional to the magnitude of the quantity, but is also influenced by other other factors for example, a radioactive substance is manufactured at a certain rate, but decays at a rate proportional to its mass, or a saver makes regular deposits in a savings account that draws compound interest. Experimental evidence shows that radioactive material decays at a rate proportional to the mass of the material present. A radioactive substance has a half-life of years.

### Exponential decay problem solving

Exponential decay is a particular form of a very rapid decrease in some quantity. One specific example of exponential decay is purified kerosene, used for jet fuel. The kerosene is purified by removing pollutants, using a clay filter.

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles. Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon. At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.

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