The rate of change with respect to time of the quantity q of pain reliever in a person's body t hours after the individual takes the medication is proportional to the quantity of medication remaining. Assume that 5 hours after a person takes 400 milligrams of a pain reliever, one-half of the original dose remains. How much pain reliever will remain after 10 hours? Round your answer to the nearest milligram.
A) 87 milligrams
B) 76 milligrams
C) 29 milligrams
D) 25 milligrams
E) 100 milligrams

Question

Quizplus · Accepted Answer

This scenario describes exponential decay, where the quantity of the pain reliever decreases by a constant percentage over equal time intervals. Given that half of the original dose remains after 5 hours, the half-life of the medication is 5 hours. Therefore, after another 5 hours (totaling 10 hours), half of the remaining 200 milligrams will be left, which is 100 milligrams.

The Rate of Change with Respect to Time of the Quantity