For children, dosage for medicine is often based on the child's mass. Let x represent a child's mass, in kilograms, and let d(x) represent the dosage, in milligrams. The function d(x) is shown for Medicines A and B. Each medicine has a maximum dosage equal to that of an adult dose.
medicine a: d(x)= [12.5x,0<x<60
750,x>60
Drag each quantity to the correct box to indicate whether it is greater for Medicine A or for Medicine B.
maxium dose, smallest mass at which maxiumm dose does occur, dosage per kilogram of mass prior to the maxiumm dosage
For Medicine A:
- Maximum dose: Medicine A has a maximum dose equal to that of an adult dose.
- Smallest mass at which the maximum dose does occur: Since the maximum dose occurs when x > 60, the smallest mass at which it occurs is 60 kg.
- Dosage per kilogram of mass prior to the maximum dosage: Prior to the maximum dosage, the dosage per kilogram of mass is given by the function d(x) = 12.5x.
For Medicine B, the information is not provided.
For Medicine A:
- Maximum dose: Medicine A has a maximum dose equal to that of an adult dose.
- Smallest mass at which maximum dose does occur: The smallest mass at which the maximum dose of Medicine A occurs is 60 kilograms.
- Dosage per kilogram of mass prior to the maximum dosage: The dosage per kilogram of mass prior to the maximum dosage of Medicine A is 12.5 milligrams.
For Medicine B:
- Maximum dose: Medicine B has a maximum dose equal to that of an adult dose.
- Smallest mass at which maximum dose does occur: The smallest mass at which the maximum dose of Medicine B occurs is not provided in the given information.
- Dosage per kilogram of mass prior to the maximum dosage: The dosage per kilogram of mass prior to the maximum dosage of Medicine B is not provided in the given information.
For Medicine A and Medicine B, we need to determine whether each quantity is greater for Medicine A or for Medicine B.
1. Maximum dose:
- Medicine A: The maximum dose for Medicine A is 750 mg.
- Medicine B: The maximum dose for Medicine B is not given.
Since the maximum dose for Medicine A is specified as 750 mg, we can conclude that the maximum dose for Medicine A is greater than the maximum dose for Medicine B (since it is not specified).
2. Smallest mass at which maximum dose does occur:
- Medicine A: The smallest mass at which the maximum dose (750 mg) occurs is not explicitly given.
- Medicine B: The smallest mass at which the maximum dose occurs is not explicitly given.
Based on the information given, we cannot determine which medicine has a smaller mass at which the maximum dose occurs. Therefore, this quantity cannot be definitively determined for either Medicine A or B.
3. Dosage per kilogram of mass prior to the maximum dosage:
- Medicine A: The dosage per kilogram of mass prior to the maximum dosage is 12.5 mg/kg for Medicine A (0 < x < 60 kg).
- Medicine B: The dosage per kilogram of mass prior to the maximum dosage is not given.
Since the dosage per kilogram of mass prior to the maximum dosage is explicitly given as 12.5 mg/kg for Medicine A, we can conclude that this quantity is greater for Medicine A compared to Medicine B (since it is not given for Medicine B).
In summary:
- Maximum dose: Greater for Medicine A.
- Smallest mass at which maximum dose does occur: Cannot determine.
- Dosage per kilogram of mass prior to the maximum dosage: Greater for Medicine A.