IAT SOLUTIONS - C_7.pdf

Chapter 7, continued53. h(x)h(x) 5 log 5 x1(5, 1)21 (1, 0)x(4, 22)(0, 23)h(x) 5 log 5 (x 1 1) 2 3Domain: x > 21Range: all real numbers54. log 279 5 x 55. log 832 5 x27 x 5 9 8 x 5 323 3x 5 3 2 2 3x 5 2 53x 5 2 3x 5 5b. M 5 0.29(ln E ) 2 9.9M 1 9.9 5 0.29(ln E )M 1 9.9} 5 ln E0.29e (M 1 9.9)/0.29) 5 EThe inverse of the function, E 5 e (M 1 9.9)/0.29) ,represents the amount of energy released (in ergs) byan earthquake of magnitude M.62. a.Copyright © by McDougal Littell, a division of Houghton Mifflin Company.x 5 2 }3x 5 5 }356. log 125625 5 x 57. log 4128 5 x125 x 5 625 4 x 5 1285 3x 5 5 4 2 2x 5 2 73x 5 4 2x 5 7x 5 4 }3P58. When P 5 57,000: h 5 28005 ln }101,300h 5 28005 ln 1 57,000 }101,3002 ø 4603x 5 7 }2The altitude is about 4603 meters above sealevel when the air pressure is 57,000 pascals.59. When H 1 5 10 22.3 : pH 5 2log[H1]pH 5 2log[10 22.3 ] 5 2.360.The pH of lemon juice is 2.3.Length (in.)l1401201008060402000 40 80 120 160 200 240 280 wWeight (lb)12 in.10 ft p } 5 120 in.1 ftUsing the graph, you can estimate that the alligatorweighs about 281 pounds when it is 10 feet (120 inches)long.61. a. When E 5 2.5 3 10 24 : M 5 0.29(ln E) 2 9.9M 5 0.29 ln (2.5310 24 ) 2 9.9ø 0.29(56.1783) 2 9.9 ø 6.39The magnitude of the earthquake was about 6.4.b. Using the graph, you can estimate that there are about15 different kinds of fish species when the area is30,000 square meters.c. Using the graph, you can estimate that the area of thelake is about 4000 square meters when there are 6species of fish.d. As the area of the pool or lake increases, the numberof fish species also increases. The answer makes sensebecause the larger the pool or lake, the more roomthere is for more varieties of fish to thrive.63. s 5 0.159 1 0.118(log d )s 2 0.159 5 0.118(log d )s 2 0.159} 5 log0.118 10ds 2 0.159}10 0.118 5 dThe inverse of the function is d 5 10 (s 2 0.159)/0.118 .When s 5 0.2: d 5 10 1 }0.2 2 0.159 20.118 ø 2.23Sand particles on a beach with a slope of 0.2 have anaverage diameter of about 2.23 millimeters.Mixed Review64. 2 3 p 2 5 5 2 3 1 5 5 2 8 5 25665. (5 23 ) 2 5 5 23 p 2 5 5 26 5 }1 5 5 16 }15,62566. 8 1 p 8 3 p 8 25 5 8 1 1 3 2 5 5 8 21 5 }1 81 } 167. 1 }5 32 23 5 }5233 5 5 3 }12523 } 5 } 5 }27 1 1 125}3 3 }2768. }10610 5 4 106 2 4 5 10 2 5 10069. (6 22 ) 21 5 6 22 p 21 5 6 2 5 3670. }424 5 5 42 2 5 5 4 23 5 }1 4 5 1 3 }6471. 1 }7872 22 5 78(22) 72169 }9(22)5 }7 7 5 218 7216 2 (218) 5 7 2 5 49Algebra 2Worked-Out Solution Key433