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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 2.2, Problem 34E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
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The table gives the number N ( t ) , measured in thousands, of minimally invasive cosmetic surgery procedures performed in the United States for various years t.

t N(t) (thousands)
2000 5, 500
2002 4, 897
2004 7, 470
2006 9, 138
2008 10, 89
2010 11, 561
2012 13, 035

Source: American Society of Plastic Surgeons

(a) What is the meaning of N ′ ( t ) ? What are its units?

(b) Construct a table of estimated values for N ′ ( t ) .

(c) Graph N and N ′ .

(d) How would it be possible to get more accurate values for N ′ ( t ) ?

(a)

To determine

To write:

the meaning of  N'(t).

The meaning of N't is the rate of change of cosmetic surgery procedures with respect to time. And its unit is number of surgery procedures (in thousands) per year.

(b)

To find:

Table of N't

t N(t)  (in thousands) N't
2000 5500  -301.5
2002 4897         1286.5
2004 7470       834
2006 9138 879.5
2008 10897 332
2010 11561 737
2012 13035

Explanation:

Formula:

N't   = Nt+h   -Nth, taking h = 2

Given: The table of Nt is given

Calculation:

We can find the values of N't by using the rate of change formula N't= Nt+h   -Nth

Where t = time is years and h = change in years

N'2000= N2002-N(2000)2=-301.5

N'2002= N2004-N(2002)2=1286.5

N'2004= N2006-N(2004)2= 834

N'2006= N2008-N(2006)2=879.5

N'2008=  N2010  - N(2008)2  = 332

N'2010= N2012-N(2010)2= 737

(c)

To graph:

N(t) and N’(t) versus t

Calculus (MindTap Course List), Chapter 2.2, Problem 34E , additional homework tip 1

Graph of N'(t)

Calculus (MindTap Course List), Chapter 2.2, Problem 34E , additional homework tip 2

(d) To explain:

how will you be able to find accurate values of N(t).

In part (b) we have calculated average rate of change in Nt.  To get more accurate value of N'(t) using the given data, we may compute two different values of rate of change for each year by using the  two different values for h namely h = 2 and h = -2, and take average of both values. Notice that this cannot be done at the end points.Thus N't   = 1/2(Nt+2   -Nt2 +Nt-2   -Nt-2 )

A more correct approach would to be sub divide the time to as small units as possible. But we do not have that data.

Explanation

Formula:

N't   = Nt+h   -Nth, taking h = 2

Given: The table of Nt is given

Calculation:

We can find the values of N't by using the rate of change formula N't= Nt+h   -Nth

Where t = time is years and h = change in years

N'2000= N2002-N(2000)2=-301.5

N'2002= N2004-N(2002)2=1286.5

N'2004= N2006-N(2004)2= 834

N'2006= N2008-N(2006)2=879

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Find the limit. Use lHospitals Rule where appropriate. If there is a more elementary method, consider using it....

Single Variable Calculus: Early Transcendentals, Volume I

Finding an Equation of a Line In Exercises 43-50, find an equation of the line that passes through the points. ...

Calculus: Early Transcendental Functions

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Calculus: An Applied Approach (MindTap Course List)

Use cylindrical or spherical coordinates, whichever seems more appropriate. 36. Find the volume of the smaller ...

Calculus: Early Transcendentals

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Precalculus: Mathematics for Calculus (Standalone Book)

Convert the expressions in Exercises 6584 to power form. 35x5x8+72x3

Finite Mathematics and Applied Calculus (MindTap Course List)

Ranking a group of cities in terms of "quality of life" would be an example of measurement on a(n)______scale o...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New...

Statistics for The Behavioral Sciences (MindTap Course List)

a. PA Compute the range, interquartile range, and standard deviation for the data presented in problem 3.4. The...

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DECLINING NUMBER of pay PHONES As cell phones proliferate, the number of pay phones continues to drop. The numb...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Explain what it means to say that limx1f(x)=3andlimx1+f(x)=7 In this situation is it possible that limx1 f(x) e...

Single Variable Calculus

Solve the equations in Exercises 112 for x (mentally, if possible). ax+b=c(a0)

Finite Mathematics

Expand Your Knowledge: Geometric Mean When data consist of percentages, ratios, compounded growth rates, or oth...

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In Exercises 17 to 24, complete each proof. Given: HF Prove: HJKFGK Exercises 19, 20 PROOF Statements Reasons 1...

Elementary Geometry For College Students, 7e

For Problems 51-78, simplify each of the numerical expressions. Objective 3 7+82

Intermediate Algebra

In Exercises 63 to 70, state the cardinality of each seL {4,6,8,10,12,...,22}

Mathematical Excursions (MindTap Course List)

Perform the indicated operations and simplify: 56+118

Elementary Technical Mathematics

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defe...

Probability and Statistics for Engineering and the Sciences

Evaluate the definite integrals in Problems 1-32. 20.

Mathematical Applications for the Management, Life, and Social Sciences

Find the first and second derivatives of the function. f(x)=0.001x50.02x3

Single Variable Calculus: Early Transcendentals

EXPLORING CONCEPTS Using Different Methods Describe two ways to find the general solution of dydx+3xy=x Verify ...

Calculus of a Single Variable

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Contemporary Mathematics for Business & Consumers

If sec=3 with in QIV, find cos, sin, and tan .

Trigonometry (MindTap Course List)

Exercise can be generalized as follows: If and the set has elements, then the number of elements of the pow...

Elements Of Modern Algebra

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Calculus: Early Transcendental Functions (MindTap Course List)

The dye dilution method is used to measure the cardiac output of a pig’s heart with 10 mg of dye. After t secon...

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The absolute maximum of f(x, y) = 12x − 8y subject to x2 + 2y2 = 11 occurs at: (3, −1) (−3, 1)

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 11 to 22, use the Given information to draw a conclusion based on the stated property or definitio...

Elementary Geometry for College Students

In Exercises 23-30, use logarithms to solve the equation for t. 5e2t=6

Finite Mathematics for the Managerial, Life, and Social Sciences

Using a Geometric Series In Exercises 35 and 36. (a) write the repeating decimal as a geometric series and (b) ...

Calculus

Finding a Conservative Vector Field In Exercises 1928, find the conservative vector field for the potential fun...

Calculus (MindTap Course List)

Using Different MethodsIn Exercises 4750, find dw/dt (a) by using appropriate Chain Rule and (b) by converting ...

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What is a ceiling effect, and how can it be a problem?

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A public utility is conducting a survey of mechanical engineers to learn more about the factors influencing the...

Statistics for Business & Economics, Revised (MindTap Course List)

Write the values of the settings on the following varnier protractor scales.

Mathematics For Machine Technology

Describe the characteristics of a within-subjects experimental research design.

Research Methods for the Behavioral Sciences (MindTap Course List)

Both surface soil and subsoil specimens were taken from eight randomly selected agricultural locations in a par...

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Find the vertex of each parabola. f(x)=2(x1)2+6

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