Practice Problem Week 3 Weight-based practice problems 1. Vibramycin 50 mg po q 12 h is ordered for a child weighing 30 lb . The recommended dosage is 2.2 to 4.4 \( \mathrm{mg} / \mathrm{kg} / \mathrm{day} \). Is the dose safe? (prove mathematically)

To determine if the dose is safe, we first need to convert the child's weight from pounds to kilograms. There are approximately 2.2 pounds in a kilogram, so: \[ 30 \, \text{lb} \times \frac{1 \, \text{kg}}{2.2 \, \text{lb}} \approx 13.64 \, \text{kg} \] Next, we'll calculate the recommended dosage range based on the child's weight: - Lower limit: \[ 2.2 \, \text{mg/kg/day} \times 13.64 \, \text{kg} \approx 29.99 \, \text{mg/day} \] - Upper limit: \[ 4.4 \, \text{mg/kg/day} \times 13.64 \, \text{kg} \approx 60.78 \, \text{mg/day} \] The total daily dose ordered is: \[ 50 \, \text{mg} \times 2 = 100 \, \text{mg/day} \] Now we compare the ordered dose to the recommended range: - Minimum recommended: Approximately 30 mg/day - Maximum recommended: Approximately 60.78 mg/day Since the ordered dose of 100 mg/day exceeds the upper limit of 60.78 mg/day, the dose is not safe.