   Chapter 11.2, Problem 71E

Chapter
Section
Textbook Problem

A patient takes 150 mg of a drug at the same time every day. Just before each tablet is taken, 5% of the drug remain in the body.(a) What quantity of the drug is in the body after the third tablet? After the nth tablet?(b) What quantity of the drug remains in the body in the long run?

To determine

Part (a):

To find:

The quantity of the drug in the body after the third tablet and nth tablet

Explanation

1) Concept:

Use a geometric series and the partial sum formula to find the quantity of the drug in the body after the third tablet and nth tablet

i) Geometric series:

n=1arn-1 =a+ar+ar2+

ii) Partial sum of geometric series:

Sn=a(1-rn)1-r

2) Given:

a=150 and r=5%=0.05

3) Calculation:

Let Q1, Q2, Q3,, Qn be the quantity of the drug in the body.

The quantity of the drug after the first tablet is taken,Q1=150 mg

Before the second tablet is taken  5% of the drug remains in the body

By using the concept

Thus, the quantity of the drug after the second tablet is taken

Q2=150+0.05Q1=150+0.05150

The quantity of the drug after third tablet is taken

Q3=150+0.05Q2= 150+1500.05+1500.052=157.875 mg

Therefore, the quantity after nth tablet is taken

Qn=150+0

To determine

Part (b):

To find:

The quantity of the drug that remains in the body in the long run.

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