Answer:
63.36 fat calories
Explanation:
The first step in determining how much of the sedative medication propofol the patient is to receive is to multiply the patient's weight in kilograms (kg) by the ordered amount for the medication. The patient weighs 80 kg and the ordered amount is 20 mcg/kg/min
80 kg × (20 mcg/kg/min)
kg in both numerator and denominator will cancel each other out, leaving mcg per min as the remaining units.
80 × 20 mcg/min
1600 mcg/min
The dosage strength, the available proportion of medication usually provided by the pharmacy, however is in milligrams per milliliter (mg/mL). So with this new proportion, a conversion factor must be used to convert micrograms (mcg) to milligrams (mg). 1 mg is equivalent to 1000 mcg, so a conversion factor of 1 mg/1000mcg can be multiplied by the above proportion.
[tex]\frac{1600 mcg}{min} (\frac{1 mg}{1000 mcg})[/tex]
mcg in both numerator and denominator will cancel each other out, leaving mg per min as the remaining units.
[tex]\frac{1600}{min} (\frac{1 mg}{1000})\\\\= \frac{1600 mg}{1000 min} = \frac{16 mg}{10 min}[/tex]
= 1.6 mg/min
This current proportion can now be multiplied by the dosage strength of the propofol, which is 10 mg/mL, to determine how much medication the patient will have infused.
[tex]\frac{1.6mg}{min} (\frac{mL}{10 mg})[/tex]
mg in both numerator and denominator will cancel each other out, leaving mL per min as the remaining units.
[tex]\frac{1.6}{min} (\frac{mL}{10})[/tex]
= 0.16 mL/min
The drip is to infuse over 6 hours. This can be converted to minutes by multiplying it by 60, because there are 60 minutes in an hour.
60 × 6 = 360 minutes
Multiply the proportion by the amount of minutes. Minutes (min) in both numerator and denominator will cancel out, leaving just how many mL of medication were infused over the 6-hour period.
0.16 mL(360) = 57.6 mL
57.6 mL of propofol were infused into the patient.
Finally, to calculate the amount of fat calories, multiply this volume by the proportion of fat calories per mL of medication. mL in both numerator and denominator will cancel out, leaving the final unit of measurement which is the desired fat calories.
57.6 mL (1.1 fat cal/mL)
57.6 × 1.1 fat cal
63.36 fat cal
The patient received 63.36 fat calories from the 6-hour propofol infusion.
