Let's work through the problem step by step:
1. Convert the weight from pounds to kilograms:
- Weight [tex]\( \text{in pounds} (lb) = 50 \)[/tex]
- To convert pounds to kilograms, we use the conversion factor [tex]\( 1 \text{ lb} = 0.453592 \text{ kg} \)[/tex].
So, the weight in kilograms:
[tex]\[
50 \, \text{lb} \times 0.453592 \, \text{kg/lb} = 22.6796 \, \text{kg}
\][/tex]
2. Calculate the daily dosage of insulin:
- The boxer needs [tex]\( 3 \, \text{IU/kg} \)[/tex] of insulin.
- The dosage is administered twice daily.
So, the total daily dosage:
[tex]\[
22.6796 \, \text{kg} \times 3 \, \text{IU/kg} \times 2 = 136.0776 \, \text{IU/day}
\][/tex]
3. Determine the total insulin needed over 4 weeks:
- There are [tex]\( 7 \)[/tex] days in a week.
- So, over 4 weeks, the total number of days is:
[tex]\[
4 \, \text{weeks} \times 7 \, \text{days/week} = 28 \, \text{days}
\][/tex]
Hence, the total insulin dosage over 4 weeks:
[tex]\[
136.0776 \, \text{IU/day} \times 28 \, \text{days} = 3810.1728 \, \text{IU}
\][/tex]
4. Convert the total insulin dosage to volume in milliliters:
- Insulin U-100 means there are 100 IU in 1 ml.
So, the volume required:
[tex]\[
\frac{3810.1728 \, \text{IU}}{100 \, \text{IU/ml}} = 38.101728 \, \text{ml}
\][/tex]
Thus, the owner will need approximately [tex]\( 38.18 \)[/tex] ml of U-100 insulin over 4 weeks.
Given the options:
1) 84 ml
2) 1.36 ml
3) 38.18 ml
4) 19.09 ml
The correct answer is:
[tex]\[ \boxed{38.18 \text{ ml}} \][/tex]
