Question

1. a doctor orders 0.2 g of rocephin to be taken by a 15 lb. 6 oz. infant every 8 hours. the recommended dosage is 75 - 100 mg/kg per day. is the ordered amount within the recommended range?

Explanation:

Step1: Convert the infant's weight to kilograms

First, convert \(15\) lb \(6\) oz to pounds. Since \(1\) oz \(=\frac{1}{16}\) lb, \(6\) oz \(=\frac{6}{16}= 0.375\) lb. So the weight \(w = 15 + 0.375=15.375\) lb. Then convert pounds to kilograms using the conversion factor \(1\) kg \( = 2.20462\) lb. So \(w=\frac{15.375}{2.20462}\approx6.97\) kg.

Step2: Calculate the ordered dosage per day

The ordered dose is \(0.2\) g every \(8\) hours. Since there are \(24\) hours in a day, the number of doses per day \(n=\frac{24}{8}=3\). The ordered dose per day \(D_{ordered}=0.2\times1000\times3\) mg (since \(1\) g \( = 1000\) mg). So \(D_{ordered}=600\) mg.

Step3: Calculate the recommended dosage range

The recommended dosage range is \(75 - 100\) mg/kg per day. For the lower - bound of the recommended dose \(D_{lower}=75\times6.97 = 522.75\) mg. For the upper - bound of the recommended dose \(D_{upper}=100\times6.97=697\) mg.

Answer:

Since \(522.75\lt600\lt697\), the ordered amount is within the recommended range.