Calculus for Business, Economics, Life Sciences and Social Sciences Books a la Carte Edition Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
13th Edition
ISBN: 9780321925718
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Textbook Question
Chapter 6.2, Problem 65E
In Problems 77–84 find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price–demand and price–supply equations. Include a graph that identifies the consumers’ surplus and the producers’ surplus. Round all values to the nearest integer.
79.p = D(x) = 80e−0.001x; p = S(x) = 30e0.001x
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Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences and Social Sciences Books a la Carte Edition Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MPCh. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MPCh. 6.1 - Prob. 1EDCh. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...
Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - Prob. 9ECh. 6.1 - A Problems 914 refer to Figures AD. Set up...Ch. 6.1 - A Problems 914 refer to Figures AD. Set up...Ch. 6.1 - A Problems 914 refer to Figures AD. Set up...Ch. 6.1 - A Problems 914 refer to Figures AD. Set up...Ch. 6.1 - A Problems 914 refer to Figures AD. 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Set up...Ch. 6.1 - B Problems 3140 refer to Figures A and B. Set up...Ch. 6.1 - B Problems 3140 refer to Figures A and B. Set up...Ch. 6.1 - B Problems 3140 refer to Figures A and B. Set up...Ch. 6.1 - B Problems 3140 refer to Figures A and B. Set up...Ch. 6.1 - Prob. 40ECh. 6.1 - Referring to Figure B, explain how you would use...Ch. 6.1 - Referring to Figure A, explain how you would use...Ch. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - In Problems 4156, find the area bounded by the...Ch. 6.1 - In Problems 4156, find the area bounded by the...Ch. 6.1 - In Problems 4156, find the area bounded by the...Ch. 6.1 - In Problems 4156, find the area bounded by the...Ch. 6.1 - In Problems 4156, find the area bounded by the...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - In Problems 5762, set up a definite integral that...Ch. 6.1 - Prob. 60ECh. 6.1 - In Problems 5762, set up a definite integral that...Ch. 6.1 - In Problems 5762, set up a definite integral that...Ch. 6.1 - In Problems 5762, set up a definite integral that...Ch. 6.1 - In Problems 5762, set up a definite integral that...Ch. 6.1 - C. In Problems 6366, find the area bounded by the...Ch. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - C. In Problems 6366, find the area bounded by the...Ch. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.1 - Prob. 81ECh. 6.1 - Prob. 82ECh. 6.1 - Prob. 83ECh. 6.1 - Prob. 84ECh. 6.1 - Oil production. Using production and geological...Ch. 6.1 - Prob. 86ECh. 6.1 - Useful life. An amusement company maintains...Ch. 6.1 - Prob. 88ECh. 6.1 - Income distribution. In a study on the effects of...Ch. 6.1 - Income distribution. Using data from the U.S....Ch. 6.1 - Distribution of wealth. Lorenz curves also can...Ch. 6.1 - Income distribution. The government of a small...Ch. 6.1 - Distribution of wealth. The data in the following...Ch. 6.1 - Prob. 94ECh. 6.1 - Biology. A yeast culture is growing at a rate of...Ch. 6.1 - Prob. 96ECh. 6.1 - Learning. A college language class was chosen for...Ch. 6.1 - Learning. Repeat Problem 91 if V(t)=13/t1/2 and...Ch. 6.2 - Matched Problem 1 (A) In Example 1, find the...Ch. 6.2 - Prob. 2MPCh. 6.2 - Prob. 3MPCh. 6.2 - Prob. 4MPCh. 6.2 - Prob. 5MPCh. 6.2 - Prob. 6MPCh. 6.2 - In Problems 18, find real numbers b and c such...Ch. 6.2 - In Problems 18, find real numbers b and c such...Ch. 6.2 - Prob. 3ECh. 6.2 - In Problems 18, find real numbers b and c such...Ch. 6.2 - In Problems 18, find real numbers b and c such...Ch. 6.2 - Prob. 6ECh. 6.2 - In Problems 18, find real numbers b and c such...Ch. 6.2 - Prob. 8ECh. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - A In Problems 914, evaluate each definite integral...Ch. 6.2 - B In Problems 15 and 16, explain which of (A),...Ch. 6.2 - B In Problems 15 and 16, explain which of (A),...Ch. 6.2 - C In Problems 1720, use a graphing calculator to...Ch. 6.2 - C In Problems 1720, use a graphing calculator to...Ch. 6.2 - C In Problems 1720, use a graphing calculator to...Ch. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Unless stated to the contrary, compute all...Ch. 6.2 - The shelf life (in years) of a laser pointer...Ch. 6.2 - 27. In Problem 25, find d so that the probability...Ch. 6.2 - Prob. 28ECh. 6.2 - A manufacturer guarantees a product for 1 year....Ch. 6.2 - In a certain city, the daily use of water (in...Ch. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Find the total income produced by a continuous...Ch. 6.2 - Find the total income produced by a continuous...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Find the total income produced by a continuous...Ch. 6.2 - Find the total income produced by a continuous...Ch. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Starting at age 25, you deposit 2,000 a year into...Ch. 6.2 - Prob. 42ECh. 6.2 - Find the future value at 3.25% interest,...Ch. 6.2 - Find the future value, at 2.95% interest,...Ch. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - An investor is presented with a choice of two...Ch. 6.2 - Prob. 48ECh. 6.2 - An investor has 10,000 to invest in either a bond...Ch. 6.2 - Prob. 50ECh. 6.2 - A business is planning to purchase a piece of...Ch. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Find the consumers surplus at a price level of...Ch. 6.2 - Find the consumers surplus at a price level of...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Find the producers surplus at a price level of P =...Ch. 6.2 - Find the producers surplus at a price level of P=...Ch. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - In Problems 7784, find the consumers surplus and...Ch. 6.2 - In Problems 7784 find the consumers surplus and...Ch. 6.2 - In Problems 7784 find the consumers surplus and...Ch. 6.2 - In Problems 80 find the consumers surplus and the...Ch. 6.2 - In Problems 7784 find the consumers surplus and...Ch. 6.2 - In Problems 82 find the consumers surplus and the...Ch. 6.2 - In Problems 83 find the consumers surplus and the...Ch. 6.2 - In Problems 84 find the consumers surplus and the...Ch. 6.2 - The following tables give pricedemand and...Ch. 6.2 - Prob. 72ECh. 6.3 - Find xe2xdx.Ch. 6.3 - Find xln2xdx.Ch. 6.3 - Find x2e2xdx.Ch. 6.3 - Find 12ln3xdx.Ch. 6.3 - Pursue choice 2 in Example 1, using the...Ch. 6.3 - Try using the integration-by-parts formula on...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - Prob. 3ECh. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - In Problems 18 find the derivative of f(x) and the...Ch. 6.3 - A In Problems 912, integrate by parts. Assume that...Ch. 6.3 - Prob. 10ECh. 6.3 - A In Problems 912, integrate by parts. 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If the marginal profit (in millions of...Ch. 6.3 - Production. An oil field is estimated to produce...Ch. 6.3 - Prob. 65ECh. 6.3 - Prob. 66ECh. 6.3 - Continuous income stream. Find the future value at...Ch. 6.3 - Continuous income stream. Find the interest earned...Ch. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - Consumers surplus. Find the consumers surplus (to...Ch. 6.3 - Prob. 76ECh. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Pollution. The concentration of particulate matter...Ch. 6.3 - Medicine. After a person takes a pill, the drug...Ch. 6.3 - Learning. A student enrolled in an advanced typing...Ch. 6.3 - Learning. A student enrolled in a stenotyping...Ch. 6.3 - Politics. The number of voters (in thousands) in a...Ch. 6.4 - Use the trapezoidal rule with n = 5 to approximate...Ch. 6.4 - Use Simpsons rule with n = 2 to approximate...Ch. 6.4 - Prob. 3MPCh. 6.4 - Prob. 4MPCh. 6.4 - Find 9x216dx.Ch. 6.4 - Find xx4+1dx.Ch. 6.4 - Prob. 7MPCh. 6.4 - Find the consumers surplus at a price level of 10...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - A In Problems 18, round function values to four...Ch. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 10ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 12ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 14ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 16ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 18ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Prob. 20ECh. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Use Table 1 on pages 547-549 to find each...Ch. 6.4 - Evaluate each definite integral in Problem 2328....Ch. 6.4 - Evaluate each definite integral in Problem 2328....Ch. 6.4 - Evaluate each definite integral in Problem 2328....Ch. 6.4 - Prob. 26ECh. 6.4 - Evaluate each definite integral in Problem 2328....Ch. 6.4 - Evaluate each definite integral in Problem 2328....Ch. 6.4 - Use the trapezoidal rule with n = 5 to approximate...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - Prob. 40ECh. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - Prob. 42ECh. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - Prob. 46ECh. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - In Problem 3950, use substitution techniques and...Ch. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - In Problems 5156, use Table 1 to find each...Ch. 6.4 - In Problems 5156, use Table 1 to find each...Ch. 6.4 - In Problems 5156, use Table 1 to find each...Ch. 6.4 - Prob. 54ECh. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - Prob. 57ECh. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - Prob. 60ECh. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - Problems 5764 are mixedsome require the use of...Ch. 6.4 - If f(x) = ax2 + bx + c, where a, b, and c are any...Ch. 6.4 - If f(x) = ax3 + bx2 + cx + d, where a, b, c, and d...Ch. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Prob. 71ECh. 6.4 - Prob. 72ECh. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - Prob. 85ECh. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Use Table 1 to evaluate all integrals involved in...Ch. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6 - In Problems 13, set up definite integrals that...Ch. 6 - In Problems 13, set up definite integrals that...Ch. 6 - In Problems 13, set up definite integrals that...Ch. 6 - Prob. 4RECh. 6 - In Problems 510, evaluate each integral. 5.xe4xdxCh. 6 - In Problems 510, evaluate each integral. 6.xlnxdxCh. 6 - In Problems 510, evaluate each integral. 7.lnxxdxCh. 6 - In Problems 510, evaluate each integral. 8.11+x2dxCh. 6 - In Problems 510, evaluate each integral....Ch. 6 - Prob. 10RECh. 6 - In Problems 1116, find the area bounded by the...Ch. 6 - In Problems 1116, find the area bounded by the...Ch. 6 - Prob. 13RECh. 6 - In Problems 1116, find the area bounded by the...Ch. 6 - Prob. 15RECh. 6 - In Problems 1116, find the area bounded by the...Ch. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - In Problems 1922, set up definite integrals that...Ch. 6 - In Problems 1922, set up definite integrals that...Ch. 6 - Prob. 21RECh. 6 - In Problems 1922, set up definite integrals that...Ch. 6 - Prob. 23RECh. 6 - In Problems 2429, evaluate each integral. 24....Ch. 6 - In Problems 24-29, evaluate each integral. 25....Ch. 6 - In Problems 2429, evaluate each integral. 26....Ch. 6 - In Problems 2429, evaluate each integral. 27....Ch. 6 - In Problems 2429, evaluate each integral. 28....Ch. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - ln Problems 3134, round function values to four...Ch. 6 - ln Problems 3134, round function values to four...Ch. 6 - ln Problems 3134, round function values to four...Ch. 6 - In Problems 3542, evaluate each integral. 35....Ch. 6 - In Problems 3542, evaluate each integral. 36....Ch. 6 - In Problems 3542, evaluate each integral. 37....Ch. 6 - In Problems 3542, evaluate each integral. 38....Ch. 6 - In Problems 3542, evaluate each integral. 39....Ch. 6 - In Problems 3542, evaluate each integral. 40....Ch. 6 - In Problems 3542, evaluate each integral. 41....Ch. 6 - In Problems 3542, evaluate each integral....Ch. 6 - Prob. 43RECh. 6 - Product warranty. A manufacturer warrants a...Ch. 6 - Product warranty. Graph the probability density...Ch. 6 - Revenue function. The weekly marginal revenue from...Ch. 6 - Continuous income stream. The rate of flow (in...Ch. 6 - Future value of a continuous income stream. The...Ch. 6 - Income distribution. An economist produced the...Ch. 6 - Consumers' and producers' surplus. Find the...Ch. 6 - Producers'surplus. The accompainying table gives...Ch. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Psychology. Rats were trained to go through a maze...
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- 150. A corporation’s annual profits and losses for a six-year period are shown in the graph inFigure 13–30.Figure 13–30a. What is the increase or decrease in profits for the years listed?(1) the 1st to the 2nd year(2) the 2nd to the 4th year(3) the 3rd to the 5th year(4) the 4th to the 6th yearb. What is the total dollar amount lost by the corporation from the 3rd through the 5th year?c. What is the net profit or loss for the 6-year period?d. What is the average annual profit or loss for the 6-year period?arrow_forward99. Unemployment. The percentage of unemployed work- ers in service occupations can be modeled by p(x) = -0.039x3 + 0.594x – 1.967x + 7.535, where x is the number of years since 2003. (Source: Based on data from www.bls.gov.) According to this model, in what year during the period 2003-2013 was this percentage a maximum?arrow_forwardWorld Population The low long-range world population numbers and projections for the years 1995–2150 are given by the equation y = -0.00036x2+0.0385x + 5.823, where x is the number of yearsafter 1990 and y is in billions. During what yearsdoes this model estimate the population to be above6 billion?arrow_forward
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- This question has several parts that must be completed sequentially. The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012. Year t (year since 2000) 0 6 12 Military Expenditure C(t)($ billion) 40 270 510 (a) Compute and interpret the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement. (b) Compute and interpret the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. Recall that the average rate of change of f(x) over the interval [a, b] is the change in f divided by the change in x. The symbol Δ means "change in." average rate of change of f = change in f change in x = Δf Δx = f(b) − f(a) b − a Note that the given chart provides data points in the form of (t, C(t)). Year t (year since 2000) 0 6 12 Military Expenditure C(t)($ billion) 40 270 510 In the…arrow_forwardInsurance Rates The following table gives themonthly insurance rates for a $100,000 life insurancepolicy for smokers 35–50 years of age.a. Create a scatter plot for the data.b. Does it appear that a quadratic function can beused to model the data? If so, find the best-fittingquadratic model.c. Find the power model that is the best fit for the data.d. Compare the two models by graphing each modelon the same axes with the data points. Whichmodel appears to be the better fit?arrow_forwardSuppose that the demand x (in units) for a product is x = 5,000 – 50p, where p dollars is the market price per unit. Then the consumer expenditure for the product is E = px = 5,000p – 50p². For what market price will expenditure be greatest? $arrow_forward
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