IAT SOLUTIONS - C_7.pdf

Chapter 7, continuedCopyright © by McDougal Littell, a division of Houghton Mifflin Company.log 3x 5 log 96xlog 36 0 log 9(6 p 6)log 36 0 log 936log 6 log 36} 0 }log 3 log 9log 6}log 3 5 }log 6log 3 ✓5log 62}log 3 2So, 6 is the solution.52. 2 2x 2 12 p 2 x 1 32 5 0(2 x 2 4)(2 x 2 8) 5 02 x 5 4 or 2 x 5 8x 5 log 24 or x 5 log 28x 5 log 22 2 or x 5 log 22 3x 5 2 or x 5 3Check: 2 2x 2 12 p 2 x 1 32 5 02 2(2) 2 12 p 2 2 1 32 0 016 2 48 1 32 0 02 2x 2 12 p 2 x 1 32 5 02 2(3) 2 12 p 2 3 1 32 0 064 2 96 1 32 0 00 5 0 ✓So, the solutions are 2 and 3.53. 5 2x 1 20 p 5 x 2 125 5 0(5 x 1 25)(5 x 2 5) 5 00 5 0 ✓5 x 5 225 or 5 x 5 5x 5 log 5(225) x 5 log 55Not defined x 5 1Check: 5 2x 1 20 p 5 x 2 125 5 05 2(1) 1 20 p 5 1 2 125 0 0So, 1 is the solution.Problem Solving25 1 100 2 125 0 00 5 0 ✓54. T 5 100, T 05 200, T R5 75, and r 5 0.054T 5 (T 02 T R)e 2rt 1 T R100 5 (200 2 75)e 20.054t 1 7525 5 125e 20.054t0.2 5 e 20.054tln 0.2 5 ln e 20.054t21.6094 ø 20.054t30 ø tIt will take about 30 minutes to cool the beef stew.55. T 5 37, T 05 75, t 5 1, and r 5 1.37T 5 (T 02 T R)e 2rt 1 T R37 5 (75 2 T R)e 21.37(1) 1 T R37 5 75e 21.37 2 T Re 21.37 1 T R37 2 75e 21.37 5 T R(2e 21.37 1 1)37 2 75e}}21.372e 21.37 1 1 5 T R37 2 75(0.25)}}20.25 1 1 ø T R24 ø T RThe outdoor temperature is about 248F.56. A 5 P 11 1 }n2 r nt When P 5 100, r 5 0.06, and A 5 1000a. When n 5 1: 1000 5 10011 1 }0.061 2 (1)t10 5 1.06 tlog10 5 log1.06 t1}log1.06 5 t1 5 tlog1.0639.5 ø tIt will take about 39.5 years for the balance toreach $1000.b. When n 5 4: 1000 5 10011 1 }0.064 2 (4)t10 5 1.015 4tlog 10 5 log 1.015 4t1}4 log 1.015 5 t1 5 4t log 1.01538.7 ø tIt will take about 38.7 years for the balance toreach $1000.c. When n 5 365: 1000 5 10011 1 }0.06365 2 (365)t10 5 1 }365.06365 2 365tlog 10 5 log 1 }365.06365 2 365t1}}365log 1 }365.06 5 t365 21 5 365t log 1 365.06 }365 238.4 ø tIt will take about 38.4 years for the balance toreach $1000.Algebra 2Worked-Out Solution Key445