To find the equivalent dose in mg/kg for a 10 lb cat, follow these steps:
1. Determine the total amount of the drug in milligrams.
- Each tablet contains 6 mg of the drug.
- The cat needs [tex]\( \frac{31}{2} \)[/tex] tablets.
- Total amount of the drug: [tex]\( \frac{31}{2} \times 6 \)[/tex] mg.
- Calculating this: [tex]\( 3.5 \times 6 = 21.0 \)[/tex] mg.
2. Convert the cat's weight from pounds to kilograms.
- The weight of the cat is 10 lb.
- The conversion factor from pounds to kilograms is [tex]\( 1 \, \text{lb} = 0.453592 \, \text{kg} \)[/tex].
- Weight in kilograms: [tex]\( 10 \, \text{lb} \times 0.453592 \, \text{kg/lb} = 4.53592 \, \text{kg} \)[/tex].
3. Calculate the dose in mg/kg.
- Total drug amount in mg: 21.0 mg.
- Weight of cat in kg: 4.53592 kg.
- Dose in mg/kg: [tex]\( \frac{21.0 \, \text{mg}}{4.53592 \, \text{kg}} = 4.629711282385933 \, \text{mg/kg} \)[/tex].
4. Compare with the given options:
- The options are:
1) 9.2 mg/kg
2) 4.6 mg/kg
3) 2.3 mg/kg
4) 1.2 mg/kg
From the calculation, the dose in mg/kg is approximately 4.63 mg/kg, which is closest to and can be rounded to 4.6 mg/kg.
Therefore, the correct answer is:
2) 4.6 mg/kg
