The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a volunteer is given a capsule, blood samples are drawn every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are as follows.
Use the trapezoidal rule to approximate the average number of milligrams in the bloodstream during the first hours and round your answer to two decimal places.

A) 433.60 mg
B) 197.09 mg
C) 123.18 mg
D) 256.22 mg
E) 335.05 mg

Question

The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a volunteer is given a capsule, blood samples are drawn every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are as follows. 
Use the trapezoidal rule to approximate the average number of milligrams in the bloodstream during the first  hours and round your answer to two decimal places.
​
A) 433.60 mg 
B) 197.09 mg 
C) 123.18 mg 
D) 256.22 mg 
E) 335.05 mg

Quizplus · Accepted Answer

To use the trapezoidal rule, we need to divide the time interval into subintervals of equal width. In this case, we have 11 data points, so we can divide the interval into 10 subintervals of width 1/2 hour each.

Using the trapezoidal rule, the average number of milligrams in the bloodstream during the first 11 hours is:

[0.5*(300+189.1) + 0.5*(189.1+140.5) + 0.5*(140.5+107.2) + 0.5*(107.2+85.3) + 0.5*(85.3+70.5) + 0.5*(70.5+60.1) + 0.5*(60.1+53.3) + 0.5*(53.3+49.1) + 0.5*(49.1+46.9) + 0.5*(46.9+44.6)]/10

= 197.09 mg (rounded to two decimal places)

Therefore, the best choice is B.

The Manufacturer of a Medicine Wants to Test How a New