Question

a doctor administers a drug to a 35-kg patient, using a dosage formula of 49 mg/kg/day. assume that the drug is available in a 200 mg per 5 ml suspension or in 300 mg tablets.
a. how many tablets should a 35-kg patient take every four hours?
b. the suspension with a drop factor of 10 gtt/ml delivers the drug intravenously to the patient over a twelve-hour period. what flow rate should be used in units of gtt/hr?
a. the patient should take 0.95 tablets every four hours.
(type an integer or decimal rounded to the nearest hundredth as needed.)
b. the intravenous suspension flow should be set to \\(\square\\) gtt/hour.
(type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Part b Solution:

Step 1: Calculate daily drug dosage

First, find the total daily dosage for the 35 - kg patient. The dosage formula is 49 mg/kg/day. So, for a 35 - kg patient, the daily dosage \(D_{daily}=49\space mg/kg/day\times35\space kg\).
\(D_{daily} = 49\times35=1715\space mg/day\)

Step 2: Dosage for 12 - hour period

Since we are dealing with a 12 - hour period, the dosage for 12 hours \(D_{12h}=\frac{1715\space mg/day}{2}\) (because 12 hours is half of a day).
\(D_{12h}=\frac{1715}{2} = 857.5\space mg\)

Step 3: Volume of suspension for 12 - hour dosage

The drug is available as a 200 mg per 5 mL suspension. Let \(V\) be the volume of the suspension needed for 857.5 mg of the drug. We can set up a proportion: \(\frac{200\space mg}{5\space mL}=\frac{857.5\space mg}{V}\). Cross - multiplying gives \(200V=857.5\times5\). Then \(V=\frac{857.5\times5}{200}=\frac{4287.5}{200} = 21.4375\space mL\)

Step 4: Calculate the number of drops (gtt) for 12 - hour period

The drop factor is 10 gtt/mL. So the number of drops \(N\) in 21.4375 mL is \(N = 10\space gtt/mL\times21.4375\space mL=214.375\space gtt\) for 12 hours.

Step 5: Calculate flow rate (gtt/hour)

To find the flow rate per hour, we divide the total number of drops in 12 hours by 12. Let \(R\) be the flow rate. \(R=\frac{214.375\space gtt}{12\space h}\approx17.86\space gtt/h\)

Answer:

17.86