265 2.5 Equations of Lines and Linear Models (a) Find a formula for C as a function of I. (b) The slope of the linear function found in part (a) is the marginal propensity to consume. What is the marginal propensity to consume for the United States from 2013–2017? 68. Concept Check A graph of y = ƒ1x2 is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ1x2 = 0? A. -15 B. 0 C. 5 D. 15 −10 −10 10 10 65. Celsius and Fahrenheit Temperatures When the Celsius temperature is 0°, the corresponding Fahrenheit temperature is 32°. When the Celsius temperature is 100°, the corresponding Fahrenheit temperature is 212°. Let C represent the Celsius temperature and F the Fahrenheit temperature. (a) Express F as an exact linear function of C. (b) Solve the equation in part (a) for C—that is, express C as a function of F. (c) For what temperature is F = C a true statement? 66. Water Pressure on a Diver The pressure P of water on a diver’s body is a linear function of the diver’s depth, x. At the water’s surface, the pressure is 1 atmosphere. At a depth of 100 ft, the pressure is about 3.92 atmospheres. (a) Find a linear function that relates P to x. (b) Compute the pressure, to the nearest hundredth, at a depth of 10 fathoms (60 ft). 67. Consumption Expenditures In Keynesian macroeconomic theory, total consumption expenditure on goods and services, C, is assumed to be a linear function of national personal income, I. The table gives the values of C and I for 2013 and 2017 in the United States (in billions of dollars). Year 2013 2017 Total consumption (C) $11,317 $13,321 National income (I) $14,495 $16,756 Data from U.S. Bureau of Economic Analysis. Use a graphing calculator to solve each linear equation. See Example 8. 69. 2x + 7 - x = 4x - 2 70. 7x - 2x + 4 - 5 = 3x + 1 71. 312x + 12 - 21x - 22 = 5 72. 4x - 314 - 2x2 = 21x - 32 + 6x + 2 73. (a) Solve -21x - 52 = -x - 2 using traditional paper-and-pencil methods. (b) Explain why the standard viewing window of a graphing calculator cannot graphically support the solution found in part (a). What minimum and maximum x-values would make it possible for the solution to be seen? 74. Use a graphing calculator to try to solve -312x + 62 = -4x + 8 - 2x. Explain what happens. What is the solution set?
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