## 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.

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 .

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?

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