   Chapter 11.2, Problem 69E

Chapter
Section
Textbook Problem

A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body.(a) How much of the drug is in the body just after the second tablet is taken? After the third tablet?(b) If Q n is the quantity of the antibiotic in the body just after the nth tablet is taken, find an equation that expresses Q n + 1 in terms of Q n .(c) What quantity of the antibiotic remains in the body in the long run?

To determine

Part (a):

To find:

The quantity of the drug in the body after the second and third tablet is taken.

Explanation

1) Concept:

Use a geometric series to find the quantity of the drug in the body after the second and third tablet is taken.

Geometric series:

n=1arn-1 =a+ar+ar2+

2) Given:

a=100 and r= 20%=0.20

3) Calculation:

Let Q1,  Q2,  Q3 be the quantity of the drug in the body after the first, second, and third tablet is taken.

The quantity of the drug in the body after the first tablet Q1=a=100 mg

Before the second tablet is taken  20% of the drug remains in the body

The quantity of the drug after the second tablet is taken

Q2=100 +0.20Q1

Now substitute Q1=100 mg in the above step

Q2=100+0

To determine

Part (b):

To find:

The equation that expresses Qn+1 in terms of Qn just after the nth tablet is taken

To determine

Part (c):

To find:

The quantity of the antibiotic that remains in the body in the long run

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 31-36 to positive exponent form. 3x4

Finite Mathematics and Applied Calculus (MindTap Course List)

Find f. f(x) = x3 + sinh x, f(0) = 1, f(2) = 2.6

Single Variable Calculus: Early Transcendentals, Volume I

Fill in each blank: 6yd4ft=ft

Elementary Technical Mathematics

Rewritten as an iterated integral in polar coordinates,

Study Guide for Stewart's Multivariable Calculus, 8th 