Young's rule is a formula that is used to calculate the appropriate dosage of a medication for a child, based on the adult dosage. The rule states that the child's dose is equal to the adult dose multiplied by the fraction of the child's age over the child's age plus 12.
Let's apply Young's rule step by step:
1. Identify the adult dose of the medication, which is given as 6.25 mg.
2. Identify the age of the child, which in this case is 8 years old.
3. Calculate the child's dose using the formula:
\[\text{Child's dose} = \text{Adult dose} \times \left(\frac{\text{Age of child}}{\text{Age of child} + 12}\right)\]
4. Plug in the values:
\[\text{Child's dose} = 6.25 \times \left(\frac{8}{8 + 12}\right)\]
\[\text{Child's dose} = 6.25 \times \left(\frac{8}{20}\right)\]
\[\text{Child's dose} = 6.25 \times 0.4\]
5. Perform the multiplication to find the child's dose before rounding:
\[\text{Child's dose} = 2.5 \text{ mg}\]
6. Round the result to the nearest hundredth, if necessary. In this case, 2.5 mg is already to the nearest hundredth.
Therefore, according to Young's rule, an 8-year-old child should be prescribed 2.5 mg of antihistamine, rounded to the nearest hundredth. The correct answer is:
3. 2.50 mg.
