## 7. Applications and Toxic Level

Using the generalized form of the sequence,

it is possible to solve questions such as the following.

Suppose the effective level for a particular drug in a particular patient is 500 mg, and dosages of 300 mg are given every 4 hours, with an initial dosage also of 300 mg. Given that the drug has a half-life of 4 hours, after which dosage will the drug first reach an effective amount in the patient's body?

Suppose instead that the effective level for the same drug as in the question above in a particular patient is 900 mg. After which dosage will the drug first reach an effective amount in the patient's body?

To visualize questions such as the one above, a simulator has been developed. You can click here to open the simulator in a new window, and here for the simulator help page. Experiment with the simulator to explore its capabilities.

On the simulator you may notice a red line labelled "toxic level", a green line labelled "effective level" and a dashed line labelled "steady state" . For now, ignore the steady state line—we will study it in the next section.

Using the simulator, set the toxic level to 100 mg, the half-life to 4 hours, pill size to 10 mg, to 3, and the number of pills to 5. After how many doses is this drug toxic?

Finally, it is important to determine the level of a drug over a longer period of time. We do this by looking at steady states, and we will formalize the mathematics of steady states in the next section.