To determine the rate of delivery in mL/hr for a 40 lb child, we need to follow these steps:
1. Convert the child's weight from pounds to kilograms:
- [tex]\(1 \text{ lb} = 0.453592 \text{ kg}\)[/tex]
- Therefore, [tex]\(40 \text{ lbs} \times 0.453592 \text{ kg/lb} = 18.14368 \text{ kg}\)[/tex]
2. Calculate the recommended dose:
- The recommended dose of penicillin is [tex]\(1.0 \text{ mg} / \text{kg} / \text{hr}\)[/tex].
- For an 18.14368 kg child, the dose is:
[tex]\[
18.14368 \text{ kg} \times 1.0 \text{ mg/kg/hr} = 18.14368 \text{ mg/hr}
\][/tex]
3. Determine the concentration of the solution:
- Given that the solution concentration is [tex]\(25 \text{ mg/mL}\)[/tex].
4. Calculate the required rate of delivery in mL/hr:
- With a concentration of [tex]\(25 \text{ mg/mL}\)[/tex], the rate of delivery is:
[tex]\[
\frac{18.14368 \text{ mg/hr}}{25 \text{ mg/mL}} = 0.7257472 \text{ mL/hr}
\][/tex]
Hence, the required rate of delivery for a 40 lb child receiving a [tex]\(25 \text{ mg/mL}\)[/tex] penicillin solution at a dose of [tex]\(1.0 \text{ mg} / \text{kg} / \text{hr}\)[/tex] is approximately [tex]\(0.7257 \text{ mL/hr}\)[/tex].
Given the options provided, none of them match our calculated value exactly. The options might be intended to mislead or there might be an error in the choices. The correct rate based on our step-by-step calculations is [tex]\(0.7257 \text{ mL/hr}\)[/tex].
