Question

an antibiotic is available in a solution with a concentration of 75 mg per 5 ml of solution or in 75 - mg capsules. the recommended dosage of the antibiotic is 15\\(\frac{mg}{kg}\\) per day. complete parts (a) and (b).
a. how many capsules should a 80 - kg person take every 3 hours?
a 80 - kg person should take 2 capsule(s) every 3 hours.
(round to the nearest integer as needed.)
b. suppose the antibiotic solution is given intravenously to a 80 - kg person over a 3 - hour period, using a microdrip system with a drop factor of 55\\(\frac{gtt}{ml}\\) (55\\(\frac{drops}{ml}\\)). what is the drop rate that should be used, in units of \\(\frac{gtt}{hr}\\) (\\(\frac{drops}{hr}\\))?
the drop rate should be \\(\square\frac{gtt}{hr}\\).
(round to the nearest integer as needed.)

Explanation:

Step1: Calculate daily dosage for 80 - kg person

The recommended dosage is $15\frac{mg}{kg}$ per day. For an 80 - kg person, the daily dosage is $15\times80 = 1200$ mg.

Step2: Calculate dosage per 3 - hour period

There are $24\div3 = 8$ three - hour periods in a day. So the dosage per 3 - hour period is $\frac{1200}{8}=150$ mg.

Step3: Calculate number of capsules per 3 - hour period (already given as 2, but showing for completeness)

Each capsule is 75 mg. So the number of capsules per 3 - hour period is $\frac{150}{75}=2$ capsules.

Step4: Calculate volume of solution for 3 - hour dosage

Since the solution has a concentration of 75 mg per 5 mL, for a 150 - mg dosage, the volume $V$ of the solution is $\frac{150}{75}\times5 = 10$ mL.

Step5: Calculate drop rate

The drop factor is 55 $\frac{gtt}{mL}$, and the time is 3 hours. The drop rate $r$ is $\frac{55\times10}{3}=\frac{550}{3}\approx183$ $\frac{gtt}{hr}$

Answer:

183