IAT SOLUTIONS - C_7.pdf

Chapter 7, continuedCopyright © by McDougal Littell, a division of Houghton Mifflin Company.63. I 5 10 3 w/m 2 ; I 05 10 212 w/m 2L(I ) 5 10 log }I 5 10 logI 01 }103102 5 10 log 212 10155 10 p 15 5 150The trumpet produces about 150 decibels of sound.64. a. Sample answer: The statement log b(M 1 N) 5log bM 1 log bN is false when b 5 2, M 5 3, and N 5 4.log 2(3 1 4) 0 log 23 1 log 24log 27 0 log 23 1 log 24log 27 0 log 23 p 4log 27 Þ log 212b. Sample answer: The statement log b(M 2 N) 5log bM 2 log bN is false when b 5 2, M 5 4, and N 5 3log 2(4 2 3) 0 log 24 2 log 23log 2(1) 0 log 24 2 log 23log 21 Þ log 24 }365. Let x 5 log bm and y 5 log bn. Then m 5 b x and n 5 b y .log bmn 5 log b(b x b y ) 5 log b(b x 1 y ) 5 x 1 y5 log bm 1 log bn66. Let x 5 log bm and y 5 log bn. Then m 5 b x and n 5 b y .b xmlog b } n 5 log b }b y 5 log b bx 2 y 5 x 2 y 5 log bm 2 log bn67. Let x 5 log bm. Then m 5 b x and m n 5 b nx .log bm n 5 log bb nx 5 nx 5 n log bm68. Let x 5 log ba, y 5 log bc, and z 5 log ca.Then a 5 b x , c 5 b y , and a 5 c z , so that b x 5 c z .x 5 log ba 5 log bb x 5 log bc z 5 zlog bc 5 zyx 5 zy → z 5 x } ylog ca 5 log b a}log bcProblem Solving69. I 5 1.4 3 10 25 w/m 2 ; I 05 10 212 w/m 2 ; n 5 3L(I ) 5 10 log }1 nII 02 5 10 log 3 3 1.4 3 10251 }}1022125 10 log 42,000,000 ø 10(7.62325) ø 76.2325The decibel level of the combined conversations in theroom is about 76 decibels.70. I 5 3.2 3 10 24 w/m 2 ; I 05 10 212 w/m 2 ; n 5 5L(I ) 5 10 log }1 nII 02 5 10 log 5 3 3.2 3 10241 }}1022125 10 log (1,600,000,000) ø 10(9.204) ø 92.04All five cars in the parking garage makeabout 92 decibels of sound.71. Increase in loudness5 L(10I ) 2 L(I )5 10 log 10I }I 02 10 log I }I 05 101log 10I }I 02 log I }I 025 101log 10 1 log I }I 02 log I }I 02Substitute.Distributive propertyProduct Property5 10 log 10 Simplify.5 10 log 1010 1 5 1The loudness increases by 10 decibels.72. Blue whale: I 5 10 6.8 w/m 2 ; I 05 10 212 w/m 2L(I ) 5 10 log1 I }I 02 5 10 log 1 }106.810 212 2ø 10 log (10 18.8 ) 5 10 p 18.8 5 188Human: I 5 10 0.8 w/m 2 ; I 05 10 212 w/m 2L(I ) 5 10log1 I }I 02 5 10log 1 }100.810 212 2 ø 10log(1012.8 )5 10 p 12.8 5 128A blue whale can produce sounds that are188 2 128 5 60 decibels louder than thoseproduced by a human.73. a. s 5 log 2f 2 5 2log 2fb. f 1.414 2.000 2.828 4.000s 1 2 3 4f 5.657 8.000 11.314 16.000s 5 6 7 8The amount of light that enters the camera increasesby about 1 each time.c. When s 5 9, an equation relating s and f is:9 5 2 log 2f9}2 5 log 2 f2 9/2 5 2 log 2 f2 9/2 5 fSo, the ninth f -stop is about 2 9/2 ø 22.627.74. a. Let h 5 original altitude, so that 2h is the doubledaltitude.Increase in speed 5 s(2h) 2 s(h)5 2 ln[100(2h)] 2 2ln (100h)5 2[ln (200h) 2 ln (100h)]5 2[ln (2 p 100h) 2 ln (100h)]5 2[ln 2 1 ln (100h) 2 ln (100h)]5 2 ln 2ø 1.39The wind speed increases by about 1.39 knots whenthe altitude doubles.Algebra 2Worked-Out Solution Key437