426 CHAPTER 3 Polynomial and Rational Functions 7. Food Bank Volunteers During the course of a year, the number of volunteers available to run a food bank each month is modeled by V1x2, where V1x2 = 2x2 - 32x + 150 between the months of January and August. Here x is time in months, with x = 1 representing January. From August to December, V1x2 is modeled by V1x2 = 31x - 226. Find the number of volunteers in each of the following months. (a) January (b) May (c) August (d) October (e) December (f) Sketch a graph of y = V1x2 for January through December. In what month are the fewest volunteers available? (a) Let x = 0 represent 1990, x = 10 represent 2000, and so on. Find a function of the form ƒ1x2 = a1x - h22 + k that models the data. Use 10, 3532 as the vertex and 1285, 20002 as another point to determine a. (b) Use the function to predict the amount of carbon dioxide in 2300. Round to the nearest unit. 8. Concentration of Atmospheric CO2 In 1990, the International Panel on Climate Change (IPCC) stated that if current trends of burning fossil fuel and deforestation were to continue, then future amounts of atmospheric carbon dioxide in parts per million (ppm) would increase, as shown in the table. Use synthetic division to perform each division. 9. x3 + x2 - 11x - 10 x - 3 10. 3x3 + 8x2 + 5x + 10 x + 2 11. 2x3 - x + 6 x + 4 12. 3x3 + 6x2 - 8x + 3 x + 3 Use synthetic division to divide ƒ1x2 by x - k for the given value of k. Then express ƒ1x2 in the form ƒ1x2 = 1x - k2q1x2 + r. 13. ƒ1x2 = 5x3 - 3x2 + 2x - 6; k = 2 14. ƒ1x2 = -3x3 + 5x - 6; k = -1 Use synthetic division to find ƒ122. 15. ƒ1x2 = -x3 + 5x2 - 7x + 1 16. ƒ1x2 = 2x3 - 3x2 + 7x - 12 17. ƒ1x2 = 5x4 - 12x2 + 2x - 8 18. ƒ1x2 = x5 + 4x2 - 2x - 4 Use synthetic division to determine whether k is a zero of the function. 19. ƒ1x2 = x3 + 2x2 + 3x + 2; k = -1 20. ƒ1x2 = 2x3 + 5x2 + 30; k = -4 21. Concept Check If ƒ1x2 is a polynomial function with real coefficients, and if 7 + 2i is a zero of the function, then what other complex number must also be a zero? Year Carbon Dioxide 1990 353 2000 375 2075 590 2175 1090 2275 2000 Data from IPCC.
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