A drug is administered every 6 hours. The kidney eliminates 55% of the drug over that period. The initial dose is 210 mg. Repeated dosage is 70 mg.

What is the "differnece equation"?

To find the difference equation, we need to understand the pattern of the drug elimination after each administration.

Let's break down the problem step by step:

1. The initial dose is 210 mg.
2. The kidney eliminates 55% of the drug over a 6-hour period, so the remaining drug after 6 hours is 210 mg * (100% - 55%) = 210 mg * 0.45 = 94.5 mg.
3. After this 6-hour period, a repeated dosage of 70 mg is administered. Therefore, the total drug in the system after each 6-hour period can be calculated by adding the remaining drug from the previous period and the repeated dosage.

Now, let's create the difference equation to represent this pattern:

Let A(n) represent the total drug in the system after the nth administration.

- For the first administration (n = 0), A(0) = 210 mg.
- For subsequent administrations (n > 0), A(n) = 0.45 * A(n-1) + 70 mg.

This is the difference equation for the drug administration scenario.