You have an ear infection and are told to take a 200 mg tablet of ampicillin (a common antibiotic) four times a day (every six hours). It is known that at the end of six hours, about 5% of the drug is still in the body. What quantity of the drug is in the body right after the the 3rd tablet?The 12th Tablet?

Assuming you continue taking tablets, what happens to the drug level in the long run?

Round your answers to three decimal places.

____ mg after the 3rd tablet
____ mg after the 12th tablet
____ mg in the long run

To calculate the quantity of the drug in the body after each tablet and in the long run, we need to account for the drug elimination and accumulation.

Here's the step-by-step explanation to find the answers:

Step 1: Determine the amount of drug remaining after each dose
After 6 hours, about 5% of the drug remains in the body. To find the remaining quantity, multiply the previous quantity by 0.95 (100% - 5%):
- After the 1st tablet: 200 mg
- After the 2nd tablet: 200 mg * 0.95 = 190 mg
- After the 3rd tablet: 190 mg * 0.95 = 180.5 mg (rounded to three decimal places)

Step 2: Calculate the quantity after the 12th tablet
Since each tablet is taken every 6 hours, the 12th tablet is taken after 12 * 6 = 72 hours. We know that after 6 hours, 5% of the drug remains. In 72 hours, we need to calculate how many 6-hour intervals have passed (72 / 6 = 12 intervals). We can use the same formula to calculate the remaining quantity:
- After the 12th tablet: 200 mg * (0.95)^12 = 123.854 mg (rounded to three decimal places)

Step 3: Determine the drug level in the long run
To analyze the long run, we can observe that each tablet taken keeps reducing the drug quantity by 5% every 6 hours, but a new tablet is also ingested every 6 hours. This means the drug level will reach a steady state eventually. In this case, we can calculate the steady state concentration by dividing the intake rate by the elimination rate.

Since we are taking 200 mg every 6 hours, the intake rate is 200 mg per 6 hours, or 200/6 = 33.333 mg per hour.

The elimination rate is calculated as the remaining percentage after each dose:
- Elimination rate = 1 - (5% / 100%) = 0.95

Now, divide the intake rate by the elimination rate to find the steady state concentration:
- Steady state concentration = 33.333 mg per hour / 0.95 = 35.032 mg per hour (rounded to three decimal places)

Therefore, in the long run, the drug quantity in the body will reach a steady state level of 35.032 mg per hour.