Morphine is administered to a patient intravenously with an initial amount of 13 mg. About 32.8% of the morphine in a patient's body is metabolized and leaves the body each hour. What is the 4-hour decay factor for the amount of morphine remaining in the body (rounded to the nearest thousandth)?
A) 2.651
B) 0.012
C) 8.736
D) 0.204
E) 0.150

Question

Quizplus · Accepted Answer

To calculate the 4-hour decay factor, we need to find out how much of the initial amount remains in the body after 4 hours.

After 1 hour, 32.8% of the initial amount is metabolized and leaves the body. This means that 67.2% remains in the body after the first hour.

After the second hour, 32.8% of the remaining amount (67.2%) is metabolized and leaves the body. Therefore, only 0.672 * 0.328 = 0.2204 or 22.04% of the initial amount is left after the second hour.

After the third hour, 32.8% of the remaining amount (77.96%) is metabolized and leaves the body. Therefore, only 0.7696 * 0.328 = 0.2525 or 25.25% of the initial amount is left after the third hour.

After the fourth hour, 32.8% of the remaining amount (74.75%) is metabolized and leaves the body. Therefore, only 0.7475 * 0.328 = 0.2451 or 24.51% of the initial amount is left after the fourth hour.

To find the decay factor, we divide the amount remaining after 4 hours by the initial amount:

Decay factor = 0.2451 / 13 = 0.01885

Rounded to the nearest thousandth, the decay factor is 0.204. Therefore, the answer is D.

Morphine Is Administered to a Patient Intravenously with an Initial