Math

CalculusApplied CalculusInflation The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007: I ( t ) CPI Dec 2006-July 2007 The approximating curve shown on the figure is given by I ( t ) = − 0.04 t 3 + 0.4 t 2 + 0.1 t + 202 ( 0 ≤ t ≤ 7 ) , where t is time in months since the start of December 2006. a. Use the model to estimate the monthly inflation rate in February 2007 ( t = 2 ) . [Recall that the inflation rate is I ′ ( t ) / I ( t ) .] b. Was inflation slowing or speeding up in February 2007? c. When was inflation speeding up? When was inflation slowing? [ HINT: See Example 3.]BuyFind*launch*

7th Edition

Waner + 1 other

Publisher: Cengage Learning,

ISBN: 9781337291248

Chapter 5.3, Problem 63E

Textbook Problem

**Inflation** The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007:

CPI Dec 2006-July 2007

The approximating curve shown on the figure is given by

where *t* is time in months since the start of December 2006.

**a.** Use the model to estimate the monthly inflation rate in February 2007
*rate* is

**b.** Was inflation slowing or speeding up in February 2007?

**c.** When was inflation speeding up? When was inflation slowing? [**HINT:** See Example 3.]

Applied Calculus

Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...

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Draw the graph of a function...Ch. 5.1 - Must endpoints always be extrema? Consider the...Ch. 5.1 - Refer to Exercises 65, and consider the function...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - For a rectangle with perimeter 20 to have the...Ch. 5.2 - For a rectangle with area 100 to have the smallest...Ch. 5.2 - Advertising Costs The cost, in thousands of...Ch. 5.2 - Advertising Costs The cost, in billions of...Ch. 5.2 - Average Cost: iPhones Assume that it costs Apple...Ch. 5.2 - Average Cost: PlayStation 4s Assume that it costs...Ch. 5.2 - Pollution Control The cost of controlling...Ch. 5.2 - Pollution Control Repeat Exercise 15 using the...Ch. 5.2 - Pollution Control (Compare Exercise 15.) 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For reasons too...Ch. 5.2 - Revenue Hercules Films is deciding on the price of...Ch. 5.2 - Profit Hercules Films is also deciding on the...Ch. 5.2 - Revenue: Smartphones Worldwide annual sales of...Ch. 5.2 - Projected Revenue: Smartphones Worldwide annual...Ch. 5.2 - Revenue: Monorail Service The demand for monorail...Ch. 5.2 - Revenue: Mars Monorail The demand for monorail...Ch. 5.2 - Revenue Assume that the demand for tuna in a small...Ch. 5.2 - Revenue In the 1930s the economist Henry Schultz...Ch. 5.2 - Revenue During the 1950s the wholesale price for...Ch. 5.2 - Revenue Your underground used-book business is...Ch. 5.2 - Profit: Smartphones (Compare Exercise 27.)...Ch. 5.2 - Projected Profit: Smartphones (Compare Exercise...Ch. 5.2 - Profit The demand equation for your companys...Ch. 5.2 - Profit Because of sales by a competing company,...Ch. 5.2 - Paint Cans A company manufactures cylindrical...Ch. 5.2 - Metal Drums A company manufactures cylindrical...Ch. 5.2 - Tin Cans A company manufactures cylindrical tin...Ch. 5.2 - Metal Drums A company manufactures cylindrical...Ch. 5.2 - Box Design Chocolate Box Company is going to make...Ch. 5.2 - Box Design Vanilla Box Company is going to make...Ch. 5.2 - Box Design A packaging company is going to make...Ch. 5.2 - Box Design A packaging company is going to make...Ch. 5.2 - Luggage Dimensions American Airlines requires that...Ch. 5.2 - Carry-on Dimensions American Airlines requires...Ch. 5.2 - Luggage Dimensions Fly-by-Night Airlines has a...Ch. 5.2 - Luggage Dimensions Fair Weather Airlines has a...Ch. 5.2 - Package Dimensions The U.S. Postal Service (USPS)...Ch. 5.2 - Package Dimensions United Parcel Service (UPS)...Ch. 5.2 - Cellphone Revenues The number of cellphone...Ch. 5.2 - Cellphone Revenues (Refer to Exercise 53.) If we...Ch. 5.2 - Research and Development Spending on research and...Ch. 5.2 - Research and Development (Refer to Exercise 55.)...Ch. 5.2 - Asset Appreciation As the financial consultant to...Ch. 5.2 - Plantation Management The value of a fir tree in...Ch. 5.2 - Marketing Strategy FeatureRich Software Company...Ch. 5.2 - Marketing Strategy FeatureRich Softwares main...Ch. 5.2 - Average Profit The FeatureRich Software Company...Ch. 5.2 - Average Profit Repeat Exercise 61 with the charge...Ch. 5.2 - Resource Allocation Your company manufactures...Ch. 5.2 - Resource Allocation Your company is the largest...Ch. 5.2 - Resource Allocation Your automobile assembly plant...Ch. 5.2 - Resource Allocation Repeat Exercise 65 using the...Ch. 5.2 - Incarceration Rate The incarceration rate (the...Ch. 5.2 - Prison Population The prison population in the...Ch. 5.2 - Embryo Development The oxygen consumption of a...Ch. 5.2 - Embryo Development The oxygen consumption of a...Ch. 5.2 - Subprime Mortgages during the Housing Bubble...Ch. 5.2 - Subprime Mortgage Debt during the Housing Bubble...Ch. 5.2 - Asset Appreciation You manage a small antique...Ch. 5.2 - Harvesting Forests The following equation models...Ch. 5.2 - Agriculture The fruit yield per tree in an orchard...Ch. 5.2 - Agriculture Two years ago, your orange orchard...Ch. 5.2 - Revenue (based on a question the GRE Economics...Ch. 5.2 - Revenue (based on a question on the GRE Economics...Ch. 5.2 - You are interested in knowing the height of the...Ch. 5.2 - You are interested in building a condominium...Ch. 5.2 - Explain why the following problem is...Ch. 5.2 - Explain why finding the production level that...Ch. 5.2 - Your friend Margo claims that all you have to do...Ch. 5.2 - Your friend Margo claims that all you have to do...Ch. 5.2 - If demand q decreases as price p increases, what...Ch. 5.2 - Explain how you would solve an optimization...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. 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M. Scherer...Ch. 5.3 - Returns on Investments A company finds that the...Ch. 5.3 - Oil Imports from Mexico Daily oil production in...Ch. 5.3 - Oil Imports from Mexico Repeat Exercises 81 using...Ch. 5.3 - Logistic Models Let f(x)=N1+Abx For constants N,...Ch. 5.3 - Logistic Models Let f(x)=N1+Aekx For constants N,...Ch. 5.3 - Population: Puerto Rico The population of Puerto...Ch. 5.3 - Population: Virgin Islands The population of...Ch. 5.3 - Asset Appreciation You manage a small antique...Ch. 5.3 - Harvesting Forests The following equation models...Ch. 5.3 - Asset Appreciation As the financial consultant to...Ch. 5.3 - Plantation Management The value of a fir tree in...Ch. 5.3 - Complete the following: If the graph of a function...Ch. 5.3 - Complete the following: If the graph of a function...Ch. 5.3 - Daily sales of Kents Tents reached a maximum in...Ch. 5.3 - The graph of daily sales of Luddingtons Wellington...Ch. 5.3 - Company As profits satisfy P(0)=1 million P(0)=1...Ch. 5.3 - Company Cs profits satisfy P(0)=1 million, P;(0)=1...Ch. 5.3 - 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End of the Earth In 5 billion years the Sun will...Ch. 5.4 - Loss of Odyssia The following graph shows the...Ch. 5.4 - Consumer Price Index The following graph shows the...Ch. 5.4 - Consumer Price Index The following graph shows the...Ch. 5.4 - Motion in a Straight Line The distance of a UFO...Ch. 5.4 - Motion in a Straight Line The distance of The Mars...Ch. 5.4 - Average Cost: iPhone Assume that is costs Apple...Ch. 5.4 - Average Cost: PlayStation 4s Assume that it costs...Ch. 5.4 - Subprime Mortgages during the Housing Bubble...Ch. 5.4 - Subprime Mortgage Debt during the Housing Bubble...Ch. 5.4 - A function is bounded if its entire graph lies...Ch. 5.4 - A function is bounded above if its entire graph...Ch. 5.4 - If the graph of a function has a vertical...Ch. 5.4 - If the graph of a function has a horizontal...Ch. 5.4 - Your friend tells you that he has found a...Ch. 5.4 - Your other friend tells you that she has found a...Ch. 5.4 - By thinking about extrema, show that, if f(x) isa...Ch. 5.4 - If f(x) isa polynomial of degree 2 or higher, show...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Sunspots The area of a circular sunspot is growing...Ch. 5.5 - Puddles The radius of a circular puddle is growing...Ch. 5.5 - Balloons A spherical party balloon is being...Ch. 5.5 - More Balloons A rather flimsy spherical balloon is...Ch. 5.5 - End of the Earth In 5 billion years the Sun will...Ch. 5.5 - End of Venus (Refer to Exercise 13.) When the Sun...Ch. 5.5 - Sliding Ladders The base of a 50-foot ladder is...Ch. 5.5 - Sliding Ladders The top of a 5-foot ladder is...Ch. 5.5 - Rising Rocket You are situated 600 meters from the...Ch. 5.5 - Descending Elevator You are situated 300 feet from...Ch. 5.5 - Average Cost The average cost function for the...Ch. 5.5 - Average Cost Repeat Exercise 19, using the revised...Ch. 5.5 - Demand Demand for your tie-dyed T-shirts is given...Ch. 5.5 - Supply The number of retro portable CD players you...Ch. 5.5 - Revenue You can now sell 50 cups of lemonade per...Ch. 5.5 - Revenue You can now sell 40 cars per month at...Ch. 5.5 - Oil Revenues Daily oil production by Pemex,...Ch. 5.5 - Oil Expenditures Daily oil imports to the United...Ch. 5.5 - Resource Allocation Your company manufactures...Ch. 5.5 - Resource Allocation Your company is the largest...Ch. 5.5 - Production The automobile assembly plant you...Ch. 5.5 - Production Refer back to the Cobb-Douglas...Ch. 5.5 - Demand Assume that the demand equation for tuna in...Ch. 5.5 - Demand The demand equation for rubies at Royal...Ch. 5.5 - Ships Sailing Apart The H.M.S. Dreadnaught is 40...Ch. 5.5 - Near Miss My aunt and I were approaching the same...Ch. 5.5 - Baseball A baseball diamond is a square with side...Ch. 5.5 - Baseball Refer to Exercise 35. Another player is...Ch. 5.5 - Movement along a Graph A point on the graph of...Ch. 5.5 - Motion around a Circle A point is moving along the...Ch. 5.5 - Education In 1991 the expected income of an...Ch. 5.5 - Education Refer back to the model in Exercise 39....Ch. 5.5 - Employment An employment research company...Ch. 5.5 - Grades A production formula for a students...Ch. 5.5 - Cones A right circular conical vessel is being...Ch. 5.5 - More Cones A circular conical vessel is being...Ch. 5.5 - Cylinders The volume of paint in a right...Ch. 5.5 - Cylinders A cylindrical bucket is being filled...Ch. 5.5 - Computers vs. Income In the 1990s the demand for...Ch. 5.5 - Computers vs. Income Refer back to the model in...Ch. 5.5 - Education and Crime The following graph compares...Ch. 5.5 - Education and Crime The following graph compares...Ch. 5.5 - Divorce Rates A study found that the divorce rate...Ch. 5.5 - Divorce Rates A study found that the divorce rate...Ch. 5.5 - Why is this section titled Related Rates?Ch. 5.5 - If you know how fast one quantity is changing and...Ch. 5.5 - In a related rates problem there is no limit to...Ch. 5.5 - If three quantities are related by a single...Ch. 5.5 - The demand and unit price for your stores...Ch. 5.5 - The number N of employees and the total floor...Ch. 5.5 - In solving a related rates problem a key step is...Ch. 5.5 - On a recent exam you were given a related rates...Ch. 5.5 - Transform the following into a mathematical...Ch. 5.5 - If two quantities x and y are related by a linear...Ch. 5.6 - Demand for Oranges The weekly sales of Honolulu...Ch. 5.6 - Demand for Oranges Repeat Exercise 1 for weekly...Ch. 5.6 - Demand for Smartphones Worldwide annual sales of...Ch. 5.6 - Projected Revenue: Smartphones Worldwide annual...Ch. 5.6 - College Tuition An old study of about 1,800 U.S....Ch. 5.6 - Monorail Services The demand for monorail service...Ch. 5.6 - Tissues The consumer demand equation for tissues...Ch. 5.6 - Bodybuilding The consumer demand curve for...Ch. 5.6 - T-Shirts The Physics Club sells E=mc2 T-shirts at...Ch. 5.6 - Comics The demand curve for original Iguanawoman...Ch. 5.6 - E-Readers The demand for Amazons Kindle e-reader...Ch. 5.6 - Monorail Service on Mars The demand for monorail...Ch. 5.6 - Corn In the 1930s the economist Henry Schultz...Ch. 5.6 - Demand for Fried Chicken A fried chicken franchise...Ch. 5.6 - Paint-By-Number The estimated monthly sales of...Ch. 5.6 - Paint-By-Number Repeat Exercise 15 using the...Ch. 5.6 - Linear Demand Functions A general linear demand...Ch. 5.6 - Exponential Demand Functions A general exponential...Ch. 5.6 - Hyperbolic Demand Functions A general hyperbolic...Ch. 5.6 - Quadratic Demand Functions A general quadratic...Ch. 5.6 - Modeling Linear Demand You have been hired as a...Ch. 5.6 - Modeling Linear Demand You have been hired as a...Ch. 5.6 - Modeling Exponential Demand As the new owner of a...Ch. 5.6 - Modeling Exponential Demand Repeat Exercise 23,...Ch. 5.6 - Income Elasticity of Demand: Live Drama The...Ch. 5.6 - Income Elasticity of Demand: Live Concerts The...Ch. 5.6 - Income Elasticity of Demand: Broadband in 2010 The...Ch. 5.6 - Income Elasticity of Demand: Broadband in 2007 The...Ch. 5.6 - Income Elasticity of Demand: Computer Usage in the...Ch. 5.6 - Income Elasticity of Demand: Internet Usage in the...Ch. 5.6 - Price Elasticity of Supply Given a supply equation...Ch. 5.6 - Price Elasticity of Supply Given a supply equation...Ch. 5.6 - Income Elasticity of Demand (based on a question...Ch. 5.6 - College Tuition (from the GRE Economics Test) A...Ch. 5.6 - Complete the following: When demand is inelastic,...Ch. 5.6 - Complete the following: When demand has unit...Ch. 5.6 - Given that the demand q is a differentiable...Ch. 5.6 - Given that the demand q is a differentiable...Ch. 5.6 - Your calculus study group is discussing price...Ch. 5.6 - Another member of your study group claims that...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 912, find the approximate...Ch. 5 - In Exercises 912, find the approximate...Ch. 5 - In Exercises 912, find the approximate...Ch. 5 - In Exercises 912, find the approximate...Ch. 5 - In Exercises 13 and 14, f is continuous on [3,3],...Ch. 5 - In Exercises 13 and 14, f is continuous on [3,3],...Ch. 5 - In Exercises 15 and 16 the position s of a point...Ch. 5 - In Exercises 15 and 16 the position s of a point...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - In Exercises 1722, sketch the graph of the given...Ch. 5 - Revenue Demand for the latest best-seller at...Ch. 5 - Revenue Demand for The Secret Loves of John O, a...Ch. 5 - Profit Taking into account storage and shipping,...Ch. 5 - Profit Taking into account storage and shipping,...Ch. 5 - Office Space Although still a sophomore at...Ch. 5 - Recreation Space As a result of complaints by the...Ch. 5 - Box Design The sales department at...Ch. 5 - Box Redesign The sales department at...Ch. 5 - Sales OHaganBooks.com modeled its weekly sales...Ch. 5 - Sales The quarterly sales of OHagan oPods...Ch. 5 - Chance Encounter Marjory Duffin is walking north...Ch. 5 - Company Logos OHaganBooks.coms website has an ani-...Ch. 5 - Elasticity of Demand (Compare Exercise 23.) Demand...Ch. 5 - Elasticity of Demand (Compare Exercise 24.) Demand...Ch. 5 - Elasticity of Demand Last year OHaganBooks.com...Ch. 5 - Elasticity of Demand JungleBooks.com (one of...

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