## 5.1 Formulating the Sequence: Part 1

In this section, we seek to generalize the process from the above sections. In particular, we seek to develop a sequence that describes the behaviour of drug levels in the body.

We first need to introduce a new variable, , to keep track of time in lieu of , which was measured in hours. will increase by for each dose taken. Thus, at , ; after the next dose, , and so on.

We let be the amount of drug in the body after dosages. We denote the initial dose, , as the time at which it is taken is at .

Figure 11 shows these changes. Specifically, it shows the change from to on the x-axis, and it shows the initial dose at , the first dose at , the second dose at and so on.

Figure 13: A plot of our sequence.

As a reminder, here are the definitions of some important parameters, which depend on the drug to be studied:

1. : is the half-life of the drug.
2. ("delta t"): is the time between doses.
3. : is the amount of active medical ingredient in one dose. For instance, if one dose consists of 2 pills with 300 mg of active ingredient each, then .

At this point, we nearly have enough information to formulate a precise sequence; however, if we look back at Figure 13, we still do not know the exact mathematical relationship that relates a value in the sequence to the next value (the expression for the y-values). In the next section, we will determine this relationship.