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U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be growing at the rate of R ( t ) = 0.063 t 2 − 0.48 t + 3.87 ( 0 ≤ t ≤ 15 ) million people/decade, where t is measured in decades, with t = 0 corresponding to 1900. Show that the average rate of growth of U.S. citizens aged 65 years and older between 2000 and 2050 will be about twice the average rate between 1950 and 2000.

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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640

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Section
BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640
Chapter 6.5, Problem 54E
Textbook Problem
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U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be growing at the rate of

R ( t ) = 0.063 t 2 0.48 t + 3.87   ( 0 t 15 )

million people/decade, where t is measured in decades, with t = 0 corresponding to 1900. Show that the average rate of growth of U.S. citizens aged 65 years and older between 2000 and 2050 will be about twice the average rate between 1950 and 2000.

To determine

To show: The average rate of the growth of U.S. citizen aged 65 years and older between 2000 and 2050 will be growing at twice the rate of that between 1950and 2000.

Explanation of Solution

Given information:

The function of the number of U.S. citizen aged 65 years older from 1900 through 2050 is given as,

R(t)=0.0063t30.48t+3.87(0t15)

Where, t is for the year and 0 for t corresponds to 1900 and function R(t) is number of U.S. citizen measured in millionpeople/decade .

Formula used:

The average value of the function R(t) is given by below formula,

AV=1baabf(x)dx .

Calculation:

Use the above formula to get the average of function R(t) between 1950 and 2000.

510R(t)dt=15510(0.063t20.48t+3.87)dt=15[(0.021)t3(0.24)t2+(3.87)t]510=15[0.021{(10)3(5)3}0.24{(10)2(5)2}+3

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Chapter 6 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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CREDIT Cards IN China The total number of credit...Ch. 6.5 - U.S. Retail E-Commerce Sales In a 2010 report,...Ch. 6.5 - International air Traffic International air...Ch. 6.5 - AVERAGE Price OF a Commodity The price of a...Ch. 6.5 - Velocity of a Falling Hammer During the...Ch. 6.5 - Waste Disposal When organic waste is dumped into a...Ch. 6.5 - Prove Property 1 of the definite integral.Ch. 6.5 - Prove Property 2 of the definite integral.Ch. 6.5 - Verify by direct computation that 13x2dx=31x2dxCh. 6.5 - Prove Property 3 of the definite integral.Ch. 6.5 - Verify by direct computation that 132xdx=219xdxCh. 6.5 - Verify by direct computation that...Ch. 6.5 - Verify by direct computation that...Ch. 6.5 - Verify by direct computation that...Ch. 6.5 - Evaluate 33(1+x)exdx.Ch. 6.5 - Evaluate 30f(x)dx, given that 03f(x)dx=4.Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - Crop YIELD If left untreated on bean stems, aphids...Ch. 6.5 - Absorption OF Drugs Jane took 100 mg of a drug in...Ch. 6.5 - Absorption OF DRUGS The concentration of a drug in...Ch. 6.6 - Suppose f and g are continuous functions such that...Ch. 6.6 - Write an expression in terms of definite integrals...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - Effect of Advertising on Revenue In the...Ch. 6.6 - Pulse Rate During Exercise In the accompanying...Ch. 6.6 - Oil Production Shortfall Energy experts disagree...Ch. 6.6 - Air Purification To study the effectiveness of air...Ch. 6.6 - Motion of Two Cars Two cars start out side by side...Ch. 6.6 - Comparison of companies revenues The rate of...Ch. 6.6 - Mexicos hedging Tactic Agustin Carstens, the...Ch. 6.6 - Turbo-charged engine versus standard Engine In...Ch. 6.6 - Alternative Energy Sources Because of the...Ch. 6.6 - Effect of TV advertising on car Sales Carl...Ch. 6.6 - Population Growth In an endeavor to curb...Ch. 6.6 - British Deficit The projected public spending by...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - The area of the region bounded by the graphs of...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - Show that the area of a region R bounded above by...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - Refer to Example 1. Find the area of the larger...Ch. 6.7 - a. Define consumers surplus. Give a formula for...Ch. 6.7 - a. Define the accumulated (future) value of an...Ch. 6.7 - Define the amount of an annuity. Give a formula...Ch. 6.7 - Explain the following terms, (a) Lorenz curve and...Ch. 6.7 - Consumers surplus The demand function for a...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Consumers Surplus It is known that the quantity...Ch. 6.7 - Producers Surplus The supplier of the portable...Ch. 6.7 - Producers Surplus The supply function for the CDs...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Producers Surplus The manufacturer of the brand of...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Producers Surplus The manufacturer of the Blu-ray...Ch. 6.7 - Consumers and producers Surplus The management of...Ch. 6.7 - Consumers and Producers Surplus The quantity...Ch. 6.7 - Refer to Example 3, page 486. Verify that...Ch. 6.7 - Future value of an Investment The newly opened...Ch. 6.7 - Future Value of an Investment An investment is...Ch. 6.7 - Present Value of an Investment Suppose an...Ch. 6.7 - Franchises Camille purchased a 15-year franchise...Ch. 6.7 - The amount of an Annuity Find the amount of an...Ch. 6.7 - The Amount of an Annuity Find the amount of an...Ch. 6.7 - Value of an Investment An investment generates a...Ch. 6.7 - Business Decisions Sharon, the owner of the...Ch. 6.7 - The Amount of an Annuity Aiso deposits 150/month...Ch. 6.7 - Custodial Accounts The Armstrongs wish to...Ch. 6.7 - Present value of an Annuity Estimate the present...Ch. 6.7 - Present Value of an Annuity Estimate the present...Ch. 6.7 - Lottery Payments A state lottery commission pays...Ch. 6.7 - Reverse Annuity Mortgages Sinclair wishes to...Ch. 6.7 - Reverse Annuity Mortgage Refer to Exercise 27....Ch. 6.7 - Gini Index The income distribution of a certain...Ch. 6.7 - Gini Index A certain countrys income distribution...Ch. 6.7 - Lorenz Curves A certain countrys income...Ch. 6.7 - Lorenz Curves A certain countrys income...Ch. 6.7 - Lorenz curves In a study conducted by a certain...Ch. 6.7 - Lorenz Curves In a study conducted by a certain...Ch. 6.7 - Re-solve Example 1, Section 6.7, using a graphing...Ch. 6.7 - Re-solve Exercise 11, Section 6.7, using a...Ch. 6.7 - The demand function for a certain brand of travel...Ch. 6.7 - Investment A is expected to generate income at the...Ch. 6.7 - Investment A is expected to generate income at the...Ch. 6 - Fill in the blanks. 1. a. A function F is an...Ch. 6 - Fill in the blanks. 2. a. cf(x)dx= b....Ch. 6 - Fill in the blanks. 3. a. A differential equation...Ch. 6 - Fill in the blanks. 4. If we let u = g(x), then du...Ch. 6 - Fill in the blanks. 5. a. If f is continuous and...Ch. 6 - Fill in the blanks. 6. a. The Fundamental Theorem...Ch. 6 - Fill in the blanks. 7. a. If f is continuous on...Ch. 6 - Fill in the blanks. 8. If f and g are continuous...Ch. 6 - Fill in the blanks. 9. a. The consumers surplus is...Ch. 6 - Fill in the blanks. 10. a. The accumulated value...Ch. 6 - Fill in the blanks. 11. The amount of an annuity...Ch. 6 - Fill in the blanks. 12. The coefficient of...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 37 and 38, refer to the following...Ch. 6 - In Exercises 37 and 38, refer to the following...Ch. 6 - Let f(x) = 2x2 + 1, and compute die Riemann sum of...Ch. 6 - Growth rue of Smartphone Users The rate of growth...Ch. 6 - Computer Resale Value Franklin National Life...Ch. 6 - Marginal Cost Functions The management of National...Ch. 6 - Marginal Revenue Functions Refer to Exercise 42....Ch. 6 - Measuring Temperature The temperature on a certain...Ch. 6 - DVD Sales The total number of DVDs sold to U.S....Ch. 6 - Air Pollution On an average summer day, the level...Ch. 6 - Marginal Cost Functions The management of a...Ch. 6 - U.S. Census The number of Americans aged 45-54...Ch. 6 - Commuter Trends Because of the increasing cost of...Ch. 6 - Supply: Womens Boots The rate of change of the...Ch. 6 - Online Retail Sales Since the inception of the...Ch. 6 - Projection TV Sales The marketing department of...Ch. 6 - Sales: Loudspeakers Sales of the Acrosonic model F...Ch. 6 - Find the area of the region under the curve y =...Ch. 6 - Find the area of the region under the curve y =...Ch. 6 - Find the area of the region bounded by the graph...Ch. 6 - Find the area of the region bounded by the curve y...Ch. 6 - Find the area of the region that is completely...Ch. 6 - Find the area of the region between the curve y =...Ch. 6 - Oil Production On the basis of current production...Ch. 6 - Find the average value of the function f(x)=xx2+16...Ch. 6 - Average Temperature The temperature (in degrees...Ch. 6 - Average Velocity of A truck A truck traveling...Ch. 6 - Membership in Credit Unions The membership in...Ch. 6 - Demand for Digital Camcorder Tapes The demand...Ch. 6 - Consumers and Producers Surplus The quantity...Ch. 6 - Retirement Account Savings Chi-Tai plans to...Ch. 6 - Installment Contracts Glenda sold her house under...Ch. 6 - Present Value of a Franchise Alicia purchased a...Ch. 6 - Income Distribution OF A Country A certain...Ch. 6 - Population Growth The population of a certain...Ch. 6 - Find (2x3+x+2x2x)dx.Ch. 6 - Find f if f(x) = ex + x and f(0) = 2.Ch. 6 - Find xx2+1dx.Ch. 6 - Evaluate 01x2x2dx.Ch. 6 - Find the area of the region completely enclosed by...

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