The total dosage of penicillin V received by a patient is proportional to the number of days the drug is administered. The recommended dosage is 500 mg per day. Which equation could be used to determine the total grams of penicillin (y) the patient receives over a certain number of days (x)? A) y = 500 x B) y = x 500 C) y = x + 500 D) y = 500x
dosage is proportional to the number of days
y = kx
...
The correct equation to determine the total grams of penicillin (y) the patient receives over a certain number of days (x) is:
D) y = 500x
To determine the equation that relates the total grams of penicillin (y) the patient receives over a certain number of days (x), we need to consider the information given.
We know that the dosage of penicillin received by the patient is proportional to the number of days the drug is administered. In other words, for each day the drug is administered, the patient receives a consistent amount of penicillin.
The recommended dosage is 500 mg per day. Since the question asks for the total grams of penicillin (y), we need to convert the milligrams to grams. There are 1000 milligrams in a gram, so the recommended dosage is 500 mg per day or 0.5 grams per day.
Now, let's establish the equation. We already know that the number of days (x) is involved, and we need the total grams of penicillin (y).
Since the dosage is consistent at 0.5 grams per day, the equation should express that the total grams (y) received by the patient is equal to the dosage per day (0.5 grams) multiplied by the number of days (x).
Therefore, the correct equation would be:
y = 0.5x
So, the correct option is B) y = x * 0.5, where the equation relates the total grams of penicillin (y) to the number of days (x) by multiplying the dosage per day (0.5 grams) by the number of days (x).