   Chapter 13.3, Problem 43E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Drug levels in the blood A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S   =   30 x 18 / 7 −   240 x 11 / 7 +   480 x 4 / 7 where x is in hours and 0   ≤   x   ≤   4 . Find the average number of milligrams of the drug in the bloodstream for the first 4 hours after a capsule is taken.

To determine

To calculate: The average number of milligrams of drug in the bloodstream for the first 4 hours after the capsule is taken where a drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S=30x18748240x117+480x47 and x is in hours and 0x4.

Explanation

Given information:

It is provided a drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S=30x18748240x117+480x47 and x is in hours and 0x4.

Formula used:

Average value

The average value of a continuous function y=f(x) over the interval [a,b] is:

Average value=1baabf(x)dx

Calculation:

The provided function is:

S=30x18748240x117+480x47

Since, the average number of milligrams of drug in the bloodstream for the first 4 hours after the capsule is taken is to be determined.

Thus, the interval is [0,4]

Consider the formula:

Average value=1baabf(x)dx

Substitute 4 for b, 0 for a and 30x18748240x117+480x47 for f(t) in above equation to get:

Average value=14004(30x18748240x117+480x47)dt=1404(30x18748240x

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