Alright, let's break down the problem step-by-step.
### Given Information:
- Gentamycin dose: 600 mg IVPB (Intravenous Piggy Back)
- Volume: 150 ml
- Infusion time: 45 minutes
- Total time considered: 24 hours
- Drip factor (microdrip): 60 gtt/ml
We need to determine:
1. The IV pump rate in ml/hr
2. The infusion rate in gtt/min
3. The total dosage the patient will receive in 24 hours
### Solution:
#### Part (a) - IV Pump Rate in ml/hr
To find the IV pump rate in milliliters per hour (ml/hr), we need to convert the total infusion time from minutes to hours and then determine how much volume is administered in one hour.
[tex]\[
\text{Infusion time in hours} = \frac{45 \text{ minutes}}{60 \text{ minutes/hour}} = 0.75 \text{ hours}
\][/tex]
The IV pump rate is calculated as follows:
[tex]\[
\text{IV Pump Rate} = \frac{\text{Total Volume}}{\text{Infusion Time in Hours}} = \frac{150 \text{ ml}}{0.75 \text{ hours}} = 200 \text{ ml/hr}
\][/tex]
#### Part (b) - Infusion Rate in gtt/min
To find the infusion rate in drops per minute (gtt/min), we use the drip factor and the total volume and time.
[tex]\[
\text{Infusion Rate} = \frac{\text{Total Volume (ml)} \times \text{Drip Factor (gtt/ml)}}{\text{Infusion Time (minutes)}} = \frac{150 \text{ ml} \times 60 \text{ gtt/ml}}{45 \text{ minutes}} = 200 \text{ gtt/min}
\][/tex]
#### Part (c) - Total Dosage in 24 Hours
First, we need to determine how many infusions occur in 24 hours. Each infusion takes 45 minutes, and we have 24 hours:
[tex]\[
\text{Number of Infusions} = \frac{24 \text{ hours}}{0.75 \text{ hours/infusion}} = 32 \text{ infusions}
\][/tex]
Since each infusion administers 600 mg of Gentamycin, the total dosage in 24 hours is:
[tex]\[
\text{Total Dosage} = \text{Dose per Infusion} \times \text{Number of Infusions} = 600 \text{ mg} \times 32 = 19200 \text{ mg}
\][/tex]
### Summary of Results:
- IV Pump Rate: 200 ml/hr
- Infusion Rate: 200 gtt/min
- Total Dosage in 24 Hours: 19200 mg
These calculations ensure that the IV infusion is accurately administered and that the patient receives the correct dosage over the course of 24 hours.
