906 CHAPTER 9 Systems and Matrices 84. In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 * 29 linear system of equations. How many arithmetic operations would this have required? Is this too many to do by hand? (Atanasoff’s work led to the invention of the first fully electronic digital computer.) (Data from The Gazette.) 85. If the number of equations and variables is doubled, does the number of arithmetic operations double? 86. Suppose that a supercomputer can execute up to 60 billion arithmetic operations per second. How many hours would be required to solve a linear system that has 100,000 variables? Atanasoff-Berry Computer Relating Concepts For individual or collaborative investigation (Exercises 87–90) (Modeling) Number of Fawns To model spring fawn count F from adult pronghorn population A, precipitation P, and severity of the winter W, environmentalists have used the equation F = a + bA + cP + dW, where a, b, c, and d are constants that must be determined before using the equation. (Winter severity is scaled between 1 and 5, with 1 being mild and 5 being severe.) Work Exercises 87–90 in order. (Data from Brase, C. and C. Brase, Understandable Statistics, D.C. Heath and Company; Bureau of Land Management.) 87. Substitute the values for F, A, P, and W from the table for Years 1–4 into the equation F = a + bA + cP + dW and obtain four linear equations involving a, b, c, and d. Year Fawns Adults Precip. (in inches) Winter Severity 1 239 871 11.5 3 2 234 847 12.2 2 3 192 685 10.6 5 4 343 969 14.2 1 5 ? 960 12.6 3 88. Write an augmented matrix representing the system in Exercise 87, and solve for a, b, c, and d. Round coefficients to three decimal places. 89. Write the equation for F using the values found in Exercise 88 for the coefficients. 90. Use the information in the table to predict the spring fawn count in Year 5. (Compare this with the actual count of 320.)
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