Question

A certain pain medication has a recommended dosage of 0.3 mg per pound of body weight, and is reported to be effective if the dosage administered is within 5% of the recommendation. Would a dosage of 50 mg be effective for a 175 pound patient?

Answer 1

To determine whether a dosage of 50 mg is effective for a 175-pound patient, we first need to calculate the recommended dosage based on the patient's weight.

1. Calculate the recommended dosage:
\[
\text{Recommended dosage} = 0.3 \, \text{mg/pound} \times 175 \, \text{pounds} = 52.5 \, \text{mg}
\]

2. Calculate the effective dosage range (within 5% of the recommended dosage):
- First, find 5% of the recommended dosage:
\[
5\% \, \text{of} \, 52.5 \, \text{mg} = 0.05 \times 52.5 \, \text{mg} = 2.625 \, \text{mg}
\]

- Then, calculate the lower and upper limits of the effective dosage:
\[
\text{Lower limit} = 52.5 \, \text{mg} - 2.625 \, \text{mg} = 49.875 \, \text{mg}
\]
\[
\text{Upper limit} = 52.5 \, \text{mg} + 2.625 \, \text{mg} = 55.125 \, \text{mg}
\]

3. Determine if the dosage of 50 mg falls within this effective range:
- The effective range is from approximately 49.875 mg to 55.125 mg.
- Since \(50 \, \text{mg}\) is greater than \(49.875 \, \text{mg}\) and less than \(55.125 \, \text{mg}\), it falls within the effective range.

Therefore, the dosage of 50 mg would be effective for a 175-pound patient.