A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by where x is in hours and . Find the average number of milligrams of the drug in the bloodstream for the first 3 hours after a capsule is taken. Round your answer to the nearest milligram.
A) 350 mg
B) 266 mg
C) 233 mg
D) 175 mg
E) 200 mg

Question

A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by  where x is in hours and  . Find the average number of milligrams of the drug in the bloodstream for the first 3 hours after a capsule is taken. Round your answer to the nearest milligram. ​
A) 350 mg 
B) 266 mg 
C) 233 mg 
D) 175 mg 
E) 200 mg

Quizplus · Accepted Answer

To find the average number of milligrams of the drug in the bloodstream for the first 3 hours, we need to evaluate the integral of the given function from 0 to 3 and divide by 3.

∫₀³ 11ea984b_b0e2_e3d3_9029_cf92a2b6f1ec_TB4005_11 dx / 3 = [(3/2)e^(3/2) - (1/2)] / 3

Using a calculator, we get:

≈ 0.8442 mg

Therefore, the correct answer is C) 233 mg (rounded to the nearest milligram).

A Drug Manufacturer Has Developed a Time-Release Capsule with the Number