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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Drug concentration A certain drug is administered once a day. The concentration of the drug in the patient’s bloodstream increases rapidly at first, but each successive does has less effect than the preceding one. The total amount of the drug (in mg) in the bloodstream after the n t h dose is given by

k = 1 n 50 ( 1 2 ) k 1

( a ) Find the amount of the drug in the bloodstream after n = 10 days.

( b ) If the drug is taken on a long- term basis, the amount in the bloodstream is approximated by the infinite series k = 1 50 ( 1 2 ) k 1 . Find the sum of this series.

To determine

(a)

To find:

The amount of drug in the patient’s bloodstream after 10 days.

Explanation

Given:

The total amount of drug in the bloodstream after the nth dose is

k1n50(12)k1

Approach:

(1) The nth partial sum of the geometric series is sn=a1rn1r;r1.

Calculation:

Calculate s10 as below.

s10=k=11050(12)k1=50+5012+50122+

To determine

(b)

To find:

The sum of the series.

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