# 5 0 5 m so the equation of the function is d t 2548 t

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505m==So, the equation of the function isD(t) = 254.8t+ 7853.For practical purposes, the graph islimited to quadrant I.(b)In the year 2015,t= 10 and thepredicted debt isD(10) = 254.8(10) + 7853 = 10,401 or\$10,401.(c)Need to findtwhereD(t) = 2(7,853) = 15,706254.8785315706254.8785330.8ttt+==Debt will be double the amount of2005 during the year 2035.40. (a)Letxdenote the number of milesdriven andC(x) the correspondingcost (in dollars).42.(a)Letxdenote the age in years of themachinery andVa linear function ofx.(b)The rental cost of a 50-mile trip isC(50) = 0.75(50) + 75 = 110.(c)125 = 0.7x+ 75, 0.7x= 50,x71.4You must drive about 72 miles.41.The slope isOriginally (when timex= 0), thevalue ofyof the books is 1,500(this is they-intercept.)+
32Chapter 1. Functions, Graphs, and Limits200()0 whenand() is19200valid for 0.19xV xxV x==(b)(4)1,900(4)20,00012,400V= −+=(c)whenx10.5, or afterabout 10.5 years.(d)Answers may vary.43. (a)Using the points (0,V) and (N,S), theslope of the line is.SVNSo, thevalue of an asset aftertyears is( ).SVB ttVN=(b)For this equipment,B(T) =6,400t+ 50,000. So,B(3) =6,400(3) + 50,000 = 30,800.Value after three years is \$30,800.44.(a)50if 1,00010,000()40if 10,00120,00035if 20,00150,000NNF NNNNN=(b)45.Let thex-axis represent time in monthsand they-axis represent price per share.(a)(b)(c)46.A rental company rents a piece ofequipment for a \$60.00 flat fee plus anhourly fee of \$5.00 per hour.(a)Lety= cost of renting the equipmentandt= number of hours.(b)
Chapter 1. Functions, Graphs, and Limits33(c)PressInputforUse dimensions [10, 10] 1 by [10,100] 10. Press.(d)To answer part (d), it may be easiest touse window dimensions [30, 33] 5 by[200, 230] 5. Press. Pressand move cross-hairs to be asclose toy= 216.25 as possible. Wheny= 216.2234, thex-coordinate is31.24. It takes approximately 31.24hours for the rental charge to be\$216.25. Using algebra, we see ittakes exactly 31.25 for the charge tobe \$216.25.47.(a)Since value doubles every 10 years,in 1910, value is \$200in 1920, value is \$400in 1930, value is \$800in 1940, value is \$1,600in 1950, value is \$3,200in 1960, value is \$6,400in 1970, value is \$12,800in 1980, value is \$25,600in 1990, value is \$51,200in 2000, value is \$102,400in 2010, value is \$204,800in 2020, value is \$409,600(b)No, it is not linear.48.(a)UseLinReg(ax+b)to obtainy= 0.245x+ 4.731.(b)According to the regression model,unemployment is changing by 0.245percentage points per year.(c)Answers will vary, but there aresignificant differences between theactual and predictedvalues.49. (a)Letxbe the number of hours spentregistering students in person. Duringthe first 4 hours(4)(35) = 140 students wereregistered. So,360140 = 220 students had pre-registered. Letybe the total numberof students who register. Then,
34Chapter 1. Functions, Graphs, and Limitsy= 35x+ 220.(b)y= (3)(35) + 220 = 325(c)From part(a), we see that220 students had pre-registered.

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Royer
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