BuyFindarrow_forward

Mathematical Applications for the ...

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

Solutions

Chapter
Section
BuyFindarrow_forward

Mathematical Applications for the ...

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

Emissions The table shows data for sulfur dioxide emissions from electricity generation (in millions of short tons) for selected years from 2000 and projected to 2035. These data can be modeled by the function

E ( x ) =   ( 0.001 x     0.062 ) ( 0.18 x 2 +   8.2 x     200 ) where x is the number of years past 2000.

(a) Find the function that models the rate of change of these emissions.

(b) Find and interpret E ' ( 20 ) .

Year Short Tons (in millions)
2000 11.4
2005 10.2
2008 7.6
2015 4.7
2020 4.2
2025 3.8
2030 3.7
2035 3.8

Source: U.S. Department of Energy

(a)

To determine

To calculate: The function that models the rate of change of emissions for the sulfur dioxide, if the function of the emission of the sulfur dioxide from electricity generation (in millions of short tons) for selected years from 2000 and projected to 2035 modeled as, E(x)=(0.001x0.062)(0.18x2+8.2x200) where x is the number of years past 2000 and the table that shows the emissions of sulfur dioxide is shown below.

Year Short Tons (in millions)
2000 11.4
2005 10.2
2008 7.6
2015 4.7
2020 4.2
2025 3.8
2030 3.7
2035 3.8
Explanation

Given Information:

The model of the emissions of sulfur dioxide is E(x)=(0.001x0.062)(0.18x2+8.2x200) and the table that gives the data for the emissions of theses sulfur dioxide with their respective years is tabulated below.

Year Short Tons (in millions)
2000 11.4
2005 10.2
2008 7.6
2015 4.7
2020 4.2
2025 3.8
2030 3.7
2035 3.8

Formula Used:

The product rule for the derivative of the two function, ddx(fg)=fdgdx+gdfdx.

The sum and difference rule of derivate of functions, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x).

The simple power rule of derivative ddx(xn)=nxn1.

Calculation:

Consider the provided function that models the rate of change of emissions for the sulfur dioxide, E(x)=(0.001x0.062)(0.18x2+8.2x200).

Differentiate the provided model function,

dE(x)dx=ddx[(0.001x0.062)(0.18x2+8.2x200)]

Use the product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fdgdx+gdfdx.

dE(x)dx=(0.001x0.062)ddx(0.18x2+8.2x200)+(0

(b)

To determine

To calculate: The rate of change of the emission of sulfur dioxide E'(20) and its interpretation.

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
Sect-9.1 P-2ESect-9.1 P-1ESect-9.1 P-4ESect-9.1 P-3ESect-9.1 P-6ESect-9.1 P-5ESect-9.1 P-8ESect-9.1 P-7ESect-9.1 P-10ESect-9.1 P-9ESect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-16ESect-9.1 P-15ESect-9.1 P-18ESect-9.1 P-17ESect-9.1 P-20ESect-9.1 P-19ESect-9.1 P-22ESect-9.1 P-21ESect-9.1 P-24ESect-9.1 P-23ESect-9.1 P-25ESect-9.1 P-26ESect-9.1 P-27ESect-9.1 P-28ESect-9.1 P-29ESect-9.1 P-30ESect-9.1 P-31ESect-9.1 P-32ESect-9.1 P-33ESect-9.1 P-34ESect-9.1 P-35ESect-9.1 P-36ESect-9.1 P-37ESect-9.1 P-38ESect-9.1 P-39ESect-9.1 P-40ESect-9.1 P-41ESect-9.1 P-42ESect-9.1 P-43ESect-9.1 P-44ESect-9.1 P-45ESect-9.1 P-46ESect-9.1 P-47ESect-9.1 P-48ESect-9.1 P-49ESect-9.1 P-50ESect-9.1 P-51ESect-9.1 P-52ESect-9.1 P-53ESect-9.1 P-54ESect-9.1 P-55ESect-9.1 P-56ESect-9.1 P-57ESect-9.1 P-58ESect-9.1 P-59ESect-9.1 P-60ESect-9.1 P-61ESect-9.1 P-62ESect-9.1 P-63ESect-9.1 P-64ESect-9.1 P-65ESect-9.1 P-66ESect-9.1 P-67ESect-9.1 P-68ESect-9.1 P-69ESect-9.1 P-70ESect-9.2 P-1CPSect-9.2 P-2CPSect-9.2 P-3CPSect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-15ESect-9.2 P-16ESect-9.2 P-17ESect-9.2 P-18ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-25ESect-9.2 P-26ESect-9.2 P-27ESect-9.2 P-28ESect-9.2 P-29ESect-9.2 P-30ESect-9.2 P-31ESect-9.2 P-32ESect-9.2 P-33ESect-9.2 P-34ESect-9.2 P-35ESect-9.2 P-36ESect-9.2 P-37ESect-9.2 P-38ESect-9.2 P-39ESect-9.2 P-40ESect-9.2 P-41ESect-9.2 P-42ESect-9.2 P-43ESect-9.2 P-44ESect-9.2 P-45ESect-9.2 P-46ESect-9.2 P-47ESect-9.2 P-48ESect-9.2 P-49ESect-9.2 P-50ESect-9.2 P-51ESect-9.2 P-52ESect-9.2 P-54ESect-9.3 P-1CPSect-9.3 P-2CPSect-9.3 P-3CPSect-9.3 P-4CPSect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-25ESect-9.3 P-26ESect-9.3 P-27ESect-9.3 P-28ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.3 P-50ESect-9.3 P-51ESect-9.3 P-52ESect-9.3 P-53ESect-9.3 P-54ESect-9.4 P-1CPSect-9.4 P-2CPSect-9.4 P-3CPSect-9.4 P-4CPSect-9.4 P-5CPSect-9.4 P-6CPSect-9.4 P-1ESect-9.4 P-2ESect-9.4 P-3ESect-9.4 P-4ESect-9.4 P-5ESect-9.4 P-6ESect-9.4 P-7ESect-9.4 P-8ESect-9.4 P-9ESect-9.4 P-10ESect-9.4 P-11ESect-9.4 P-12ESect-9.4 P-13ESect-9.4 P-14ESect-9.4 P-15ESect-9.4 P-16ESect-9.4 P-17ESect-9.4 P-18ESect-9.4 P-19ESect-9.4 P-20ESect-9.4 P-21ESect-9.4 P-22ESect-9.4 P-23ESect-9.4 P-24ESect-9.4 P-25ESect-9.4 P-26ESect-9.4 P-27ESect-9.4 P-28ESect-9.4 P-29ESect-9.4 P-30ESect-9.4 P-31ESect-9.4 P-32ESect-9.4 P-33ESect-9.4 P-34ESect-9.4 P-35ESect-9.4 P-36ESect-9.4 P-37ESect-9.4 P-38ESect-9.4 P-39ESect-9.4 P-40ESect-9.4 P-41ESect-9.4 P-42ESect-9.4 P-43ESect-9.4 P-44ESect-9.4 P-45ESect-9.4 P-46ESect-9.4 P-47ESect-9.4 P-48ESect-9.4 P-49ESect-9.4 P-50ESect-9.4 P-51ESect-9.4 P-52ESect-9.4 P-53ESect-9.4 P-54ESect-9.4 P-55ESect-9.4 P-56ESect-9.4 P-57ESect-9.4 P-58ESect-9.5 P-1CPSect-9.5 P-2CPSect-9.5 P-3CPSect-9.5 P-4CPSect-9.5 P-5CPSect-9.5 P-2ESect-9.5 P-1ESect-9.5 P-4ESect-9.5 P-3ESect-9.5 P-5ESect-9.5 P-6ESect-9.5 P-8ESect-9.5 P-7ESect-9.5 P-9ESect-9.5 P-10ESect-9.5 P-11ESect-9.5 P-12ESect-9.5 P-13ESect-9.5 P-14ESect-9.5 P-15ESect-9.5 P-16ESect-9.5 P-17ESect-9.5 P-18ESect-9.5 P-19ESect-9.5 P-20ESect-9.5 P-21ESect-9.5 P-22ESect-9.5 P-23ESect-9.5 P-24ESect-9.5 P-25ESect-9.5 P-26ESect-9.5 P-27ESect-9.5 P-28ESect-9.5 P-29ESect-9.5 P-30ESect-9.5 P-35ESect-9.5 P-36ESect-9.5 P-37ESect-9.5 P-38ESect-9.5 P-39ESect-9.5 P-40ESect-9.5 P-41ESect-9.5 P-42ESect-9.5 P-43ESect-9.5 P-44ESect-9.5 P-45ESect-9.5 P-46ESect-9.5 P-47ESect-9.5 P-48ESect-9.5 P-49ESect-9.5 P-50ESect-9.5 P-51ESect-9.5 P-52ESect-9.5 P-53ESect-9.5 P-54ESect-9.5 P-55ESect-9.5 P-56ESect-9.6 P-1CPSect-9.6 P-2CPSect-9.6 P-1ESect-9.6 P-2ESect-9.6 P-3ESect-9.6 P-4ESect-9.6 P-5ESect-9.6 P-6ESect-9.6 P-7ESect-9.6 P-8ESect-9.6 P-9ESect-9.6 P-10ESect-9.6 P-11ESect-9.6 P-12ESect-9.6 P-13ESect-9.6 P-14ESect-9.6 P-15ESect-9.6 P-16ESect-9.6 P-17ESect-9.6 P-18ESect-9.6 P-19ESect-9.6 P-20ESect-9.6 P-21ESect-9.6 P-22ESect-9.6 P-23ESect-9.6 P-24ESect-9.6 P-25ESect-9.6 P-26ESect-9.6 P-27ESect-9.6 P-28ESect-9.6 P-29ESect-9.6 P-30ESect-9.6 P-31ESect-9.6 P-32ESect-9.6 P-33ESect-9.6 P-34ESect-9.6 P-35ESect-9.6 P-36ESect-9.6 P-37ESect-9.6 P-38ESect-9.6 P-39ESect-9.6 P-40ESect-9.6 P-41ESect-9.6 P-42ESect-9.6 P-43ESect-9.6 P-44ESect-9.6 P-45ESect-9.6 P-46ESect-9.6 P-47ESect-9.6 P-48ESect-9.6 P-49ESect-9.6 P-50ESect-9.6 P-51ESect-9.6 P-52ESect-9.6 P-53ESect-9.6 P-54ESect-9.6 P-55ESect-9.6 P-56ESect-9.7 P-1CPSect-9.7 P-2CPSect-9.7 P-3CPSect-9.7 P-1ESect-9.7 P-2ESect-9.7 P-3ESect-9.7 P-4ESect-9.7 P-5ESect-9.7 P-6ESect-9.7 P-7ESect-9.7 P-8ESect-9.7 P-9ESect-9.7 P-10ESect-9.7 P-11ESect-9.7 P-12ESect-9.7 P-13ESect-9.7 P-14ESect-9.7 P-15ESect-9.7 P-16ESect-9.7 P-17ESect-9.7 P-18ESect-9.7 P-19ESect-9.7 P-20ESect-9.7 P-21ESect-9.7 P-22ESect-9.7 P-23ESect-9.7 P-24ESect-9.7 P-25ESect-9.7 P-26ESect-9.7 P-27ESect-9.7 P-28ESect-9.7 P-29ESect-9.7 P-30ESect-9.7 P-31ESect-9.7 P-32ESect-9.7 P-33ESect-9.7 P-34ESect-9.7 P-35ESect-9.7 P-36ESect-9.7 P-37ESect-9.7 P-38ESect-9.7 P-39ESect-9.7 P-40ESect-9.7 P-41ESect-9.7 P-42ESect-9.7 P-43ESect-9.7 P-44ESect-9.7 P-45ESect-9.8 P-1CPSect-9.8 P-2CPSect-9.8 P-3CPSect-9.8 P-4CPSect-9.8 P-1ESect-9.8 P-2ESect-9.8 P-3ESect-9.8 P-4ESect-9.8 P-5ESect-9.8 P-6ESect-9.8 P-7ESect-9.8 P-8ESect-9.8 P-9ESect-9.8 P-10ESect-9.8 P-11ESect-9.8 P-12ESect-9.8 P-13ESect-9.8 P-14ESect-9.8 P-15ESect-9.8 P-16ESect-9.8 P-17ESect-9.8 P-18ESect-9.8 P-19ESect-9.8 P-20ESect-9.8 P-21ESect-9.8 P-22ESect-9.8 P-23ESect-9.8 P-24ESect-9.8 P-25ESect-9.8 P-26ESect-9.8 P-27ESect-9.8 P-28ESect-9.8 P-29ESect-9.8 P-30ESect-9.8 P-31ESect-9.8 P-32ESect-9.8 P-33ESect-9.8 P-34ESect-9.8 P-35ESect-9.8 P-36ESect-9.8 P-37ESect-9.8 P-38ESect-9.8 P-39ESect-9.8 P-40ESect-9.8 P-41ESect-9.8 P-42ESect-9.8 P-43ESect-9.8 P-44ESect-9.8 P-47ESect-9.9 P-1CPSect-9.9 P-2CPSect-9.9 P-3CPSect-9.9 P-4CPSect-9.9 P-5CPSect-9.9 P-6CPSect-9.9 P-7CPSect-9.9 P-1ESect-9.9 P-2ESect-9.9 P-3ESect-9.9 P-4ESect-9.9 P-5ESect-9.9 P-6ESect-9.9 P-7ESect-9.9 P-8ESect-9.9 P-9ESect-9.9 P-10ESect-9.9 P-11ESect-9.9 P-12ESect-9.9 P-13ESect-9.9 P-14ESect-9.9 P-15ESect-9.9 P-16ESect-9.9 P-17ESect-9.9 P-18ESect-9.9 P-19ESect-9.9 P-20ESect-9.9 P-21ESect-9.9 P-22ESect-9.9 P-23ESect-9.9 P-24ESect-9.9 P-25ESect-9.9 P-26ESect-9.9 P-27ESect-9.9 P-28ESect-9.9 P-29ESect-9.9 P-30ESect-9.9 P-31ESect-9.9 P-32ESect-9.9 P-33ESect-9.9 P-34ESect-9.9 P-35ESect-9.9 P-36ESect-9.9 P-37ESect-9.9 P-38ECh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-11RECh-9 P-12RECh-9 P-13RECh-9 P-14RECh-9 P-15RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-25RECh-9 P-26RECh-9 P-27RECh-9 P-28RECh-9 P-29RECh-9 P-30RECh-9 P-31RECh-9 P-32RECh-9 P-33RECh-9 P-34RECh-9 P-35RECh-9 P-36RECh-9 P-37RECh-9 P-38RECh-9 P-39RECh-9 P-40RECh-9 P-41RECh-9 P-42RECh-9 P-43RECh-9 P-44RECh-9 P-45RECh-9 P-46RECh-9 P-47RECh-9 P-48RECh-9 P-49RECh-9 P-50RECh-9 P-51RECh-9 P-52RECh-9 P-53RECh-9 P-54RECh-9 P-55RECh-9 P-56RECh-9 P-57RECh-9 P-58RECh-9 P-59RECh-9 P-60RECh-9 P-61RECh-9 P-62RECh-9 P-63RECh-9 P-64RECh-9 P-65RECh-9 P-66RECh-9 P-67RECh-9 P-68RECh-9 P-69RECh-9 P-70RECh-9 P-71RECh-9 P-72RECh-9 P-73RECh-9 P-74RECh-9 P-75RECh-9 P-76RECh-9 P-77RECh-9 P-78RECh-9 P-79RECh-9 P-80RECh-9 P-81RECh-9 P-82RECh-9 P-83RECh-9 P-84RECh-9 P-85RECh-9 P-86RECh-9 P-87RECh-9 P-88RECh-9 P-89RECh-9 P-90RECh-9 P-91RECh-9 P-92RECh-9 P-93RECh-9 P-94RECh-9 P-95RECh-9 P-96RECh-9 P-97RECh-9 P-98RECh-9 P-99RECh-9 P-100RECh-9 P-101RECh-9 P-102RECh-9 P-103RECh-9 P-104RECh-9 P-105RECh-9 P-106RECh-9 P-107RECh-9 P-108RECh-9 P-1TCh-9 P-2TCh-9 P-3TCh-9 P-4TCh-9 P-5TCh-9 P-6TCh-9 P-7TCh-9 P-9TCh-9 P-10TCh-9 P-11TCh-9 P-12TCh-9 P-13TCh-9 P-14T

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 75-98, perform the indicated operations and/or simplify each expression. 89. (x + 2y)2

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

Divide: +4800240

Elementary Technical Mathematics

Verify each identity. cotx=cos3x+cosxsin3xsinx

Trigonometry (MindTap Course List)

In Exercise 1-22, evaluate the given expression. P(n,n2)

Finite Mathematics for the Managerial, Life, and Social Sciences

Solve Exercise 55 when |CD| = 2 cm.

Single Variable Calculus: Early Transcendentals

The vector c in the figure at the right is: a – b b − a a + b 2a – b

Study Guide for Stewart's Multivariable Calculus, 8th

Use a Table of Integrals to evaluate .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th