Pre-Calc Homework Solutions 30

Pre-Calc Homework Solutions 30 - 30 Section 1.5 45. (a) f (...

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Unformatted text preview: 30 Section 1.5 45. (a) f ( f(x)) x 44. y 1 1.1 1 50 1.1 x 1 1 x2 ( f (x))2 (1 x 1 1/x x 2) x, since x x for all x 0 0 1.1 x 50 y 50 y x 1 50 log1.1 y (b) f( f(x)) 1 46. (a) Amount log1.1 50 y y f log1.1(1.1 ) x x log1.1 50 y 50 log1.1 y 1 x 1 1 log1.1 y 50 y 8 1 t/12 2 (b) 8 1 t/12 2 1 1 8 1 3 2 Interchange x and y: y f 1 log1.1 (x) x 50 x x 50 x x 50 x log1.1 Verify. (f f 1 1 t/12 2 1 t/12 2 t 3 12 t 36 )(x) f log1.1 There will be 1 gram remaining after 36 hours. 47. 500(1.0475)t x 50 1 1.1 log1.1 50 x 1000 1.0475t t 2 ln 2 ln 2 14.936 ln(1.0475 ) 50 1 1.1log1.1 50 x x t ln 1.0475 t ln 2 ln 1.0475 50 1 50 x x It will take about 14.936 years. (If the interest is paid at the end of each year, it will take 15 years.) 48. 375,000(1.0225)t 1,000,000 x 50x (50 x) 50x 50 x 1.0225t 8 3 8 3 8 ln 3 ln(1.0225t) t ln 1.0225 (f 1 ln f )(x) f 1 1 50 1.1 x t ln(8/3) ln 1.0225 44.081 It will take about 44.081 years. 50 1 1.1 x log1.1 50 50 1 1.1 49. (a) y x 2539.852 636.896 ln x (b) When x 75, y 209.94. About 209.94 million metric tons were produced. (c) 50 log1.1 50(1 50 1.1 x) 2539.852 636.896 ln x 636.896 ln x ln x 400 2939.852 2939.852 636.896 log1.1 1 1.1 x log1.1(1.1x) x x e 636.896 2939.852 101.08 According to the regression equation, Saudi Arabian oil production will reach 400 million metric tons when x 101.08, in about 2001. ...
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