IAT SOLUTIONS - C_7.pdf

Chapter 7, continuedCopyright © by McDougal Littell, a division of Houghton Mifflin Company.5. (25e 3x ) 3 5 25 3 (e 3x ) 3 5 2125e 9x6. }e4x5e 5 }1 5 e4x 2 1 7. }8e5x6e8.211yx9.5 4e5x 2 2x2x }2131y5 4e3x }3Domain: all real numbers Domain: all real numbersRange: y > 0 Range: y > 010.y11.g(x)2(1, 2.72)(0, 1)y 5 e x (0, 0.72)(21, 21) 1 xy 5 e x 1 1 2 2(0, 4)211(0, 5)g(x) 5 4e 23x 1 1(1, 1.20)(1, 0.20)xg(x) 5 4e 23xDomain: all real numbers Domain: all real numbersRange: y > 22 Range: y > 112. Decay factor 5 0.85;percent decrease 5 1 2 0.85 5 0.15nDomain: 0, 1, 2, 3, 430Range: 26.8, 22.8, 19.4,2016.5, 14.0; using thegraph you can estimate10that the number of0black-and-white TVs0 2 4 6 8 tsold in 1999 (t 5 2) wasYears since 1997about 19 million.13. When P 5 1200, r 5 0.045, and t 5 5: A 5 Pe rtA 5 1200e (0.045)(5) 5 1200e (0.225) ø 1502.79The balance after 5 years is $1502.79.TVs sold (millions)Lesson 7.47.4 Guided Practice (pp. 499 – 503)1. log 381 5 4 2. log 77 5 13 4 5 81 7 1 5 73. log 141 5 0 4. log 1/232 5 2514 0 5 1 1 }1 22 25 5 325. 2 5 5 32, so log 232 5 5 6. 27 1/3 5 3, so log 273 5 }1 37. log 12 ø 1.079 8. ln 0.75 ø 20.2889. s 5 93 log d 1 65 5 93 log 150 1 65ø 93(2.176) 1 65 5 267.368The wind speed near the tornado’s center is about267 miles per hour10. 8 log 8 x 5 x 11. log 77 23x 5 23x12. log 264 x 5 log 22 6x 5 6x 13. e ln 20 5 e log e 20 5 20x14. From the definition of logorithm, the inverseof y 5 4 x is y 5 log 4x.15. y 5 ln (x 2 5)x 5 ln ( y 2 5)e x 5 y 2 5e x 1 5 5 yThe inverse of y 5 ln (x 2 5) is y 5 e x 1 5.16. y11Domain: x > 0Range: all real numbers17. y y 5 log 1/3 (x 2 3)11( 9 , 2 )28( 9 , 2 )10( 3 , 1 )1( 3 , 1 )(4, 0)(1, 0)1y 5 log 1/3 xDomain: x > 3Range: all real numbers18. f(x)222(1, 0)(4, 1)(0, 22)(15, 0) x(3, 21)xf(x) 5 log 4 x(16, 2)f(x) 5 log 4 (x 1 1) 2 2Domain: x > 21Range: all real numbers7.4 Exercises (pp. 503 – 505)Skill Practice1. A logarithm with base 10 is called a(n) commonlogarithm.2. From the definition of logarithm, the inverse of y 5 5 x isy 5 log 5x, so y 5 5 x and y 5 log 5x are inverses.3. log 416 5 2 4. log 7343 5 34 2 5 16 7 3 5 34315. log 6 }36 5 22 6. log 64 1 5 06 22 5 }1 64 0 5 1367. The 23 and }1 8 should be switched. Because 223 5 }1 8 ,1the equation should be log 2 }8 5 23.8. 15 1 5 15, so log 1515 5 1.9. 7 2 5 49, so log 749 5 2.10. 6 3 5 216, so log 6216 5 3.xAlgebra 2Worked-Out Solution Key431