Appendix: 2. Exponential Decay

In the previous section, we introduced the equation that governs exponential decay: as well .

What is the effect of ? What occurs if is small? If is large?

To answer these questions, we need a mathematical way to compare the curves generated by various values of . To do so, we consider , or in other words, half of the initial value. must occur for some specific time, which we will denote . This is shown below in Figure 2.

Figure 2: and .

is an important value, and it is known as half-life. It is the time at which the initial value o the substance has decreased by half.

Now we can consider the effect of on the behaviour of the curve. Below is a diagram, in which two curves are shown. Compare the values of with the relative size of .

Figure 3: Exponential decay curves for and

Thus, for large , we have small and for small we have a large .

Opportunity for a question... What happens to as gets larger and larger?

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In the next section we will explore the relation between and .