IAT SOLUTIONS - C_7.pdf

Chapter 7, continued3. Sample answer:Known point: (2, 7) Another point: (4, 112)(2, 7): 7 5 ab 2 → a 5 }7 b 2(4, 112): 112 5 ab 44. A logarithm with base e is called a natural logarithm.5. y 5 (1.4) x is an exponential function because it has theform y 5 ab x .6.y7.yCopyright © by McDougal Littell, a division of Houghton Mifflin Company.112 5 1 7 }b 2 2 b4112 5 7b 216 5 b 24 5 ba 5 }7 b 5 7 2 }4 5 7 2 }16An equation is y 5 }7 16 p 4x .4. When you look at the graphs of (x, ln y) and(ln x, ln y), graph of (ln x, ln y) appears to be more linearthan the graph of (x, ln y). So, a power model wouldbetter fit the data.5. a. When N 5 0.05: N 5 ln (E 1 1)0.05 5 ln (E 1 1)e 0.05 5 E 1 1e 0.05 2 1 5 Eb. When N 5 0.1: N 5 ln (E 1 1)0.1 5 ln (E 1 1)e 0.1 5 E 1 1e 0.1 2 1 5 EE from part (b)c. }}E from part (a) 5 e0.1 2 1}e 0.05 2 1e 0.1 2 1d. } 0 e 0.05 1 1e 0.05 2 1(e 0.05 2 1) 1 e0.01 2 1}e 0.05 2 12 0 (e 0.05 2 1)(e 0.05 1 1)e 0.1 2 1 0 e 2(0.05) 1 e 0.05 2 e 0.05 2 1e 0.1 2 1 5 e 0.1 2 1 ✓6. When P 5 4000, r 5 0.02, andA 5 4000 1 1000 5 5000:A 5 Pe rt5000 5 4000e (0.02)t1.25 5 e 0.02tln 1.25 5 0.02t0.22 ø 0.02t11 ø tIt will take about 11 years to earn $1000 interest.Chapter 7 Review (pp. 539–542)1. The asymptote of the function y 5 221 }1 42 x 1 1 1 5is y 5 5.2. The decay factor in the model y 5 7.2(0.89) x is 0.89.3. Sample answer: log by represents the logarithm of y withbase b, and it is equal to x if and only if b x 5 y.212xDomain: all real numbers Domain: all real numbersRange: y > 0 Range: y > 08.3 f(x)f(x) 5 23 ? 4 x( 21, 24 )( 22, 2114 )(21, 25)f(x) 5 23 ? 4 x 1 1 2 211(0, 23)Domain: all real numbersRange: y < 229. When P 5 1500, r 5 0.07n 5 365, and t 5 2:A 5 P 11 1 } n r 2 ntA 5 150011 1 }0.07365 2 365 p 25 15001 }365.07365 2 730ø 1725.39The balance after 2 years is $1725.39.y10.11.211xx(0, 23)21yy 5(0, 1)1y 5211( 3)x1( 1,3 )( 1, 2113 )1( ) x 3 2 4Domain: all real numbers Domain: all real numbersRange: y > 0 Range: y > 2412.f(x)13.yf(x) 5 2(0.8) x 2 1 1 3(1, 5)(2, 4.6)(0, 2) f(x) 5 2(0.8) x(1, 1.6)211xDomain: all real numbers Domain: all real numbersRange: y > 3 Range: y > 0211xxxAlgebra 2Worked-Out Solution Key461