Concept explainers
Nebraska The 1970 economy of the state of Nebraska has been condensed to six sectors: livestock, crops, food products, mining and manufacturing, households, and other. The input–output matrix is given below. Source: University of Nebraska-Lincoln.
- (a) Find the matrix (I − A)−1 and interpret the value in row 2, column 1 of this matrix.
- (b) Suppose the demand (in millions of dollars) is
Find the dollar amount of each commodity that should be produced.
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Chapter 2 Solutions
Finite Mathematics and Calculus with Applications
- Oil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forwardMale and female populations of tortoises under 80 years old are represented by age in the table below. Complete parts (a) through (d).arrow_forwardslove.arrow_forward
- Future Demographics The tables below show important demographics for China, Bangladesh, and thePhilippines for 2012 and projected for 2062.a. Create matrix B for the 2012 table and matrix Afor the 2062 table.b. Find a matrix C that shows the changes of demographics from 2012 to 2062 for these countries.c. Which negative entries in matrix C definitelyindicate a positive change for the countries?arrow_forwardhelp. upvote guaranteedarrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,