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Pre-Calc Homework Solutions 30

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

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44. y 5 } 1 1 5 1 0 .1 2 x } 1 1 1.1 2 x 5 } 5 y 0 } 1.1 2 x 5 } 5 y 0 } 2 1 log 1.1 (1.1 2 x ) 5 log 1.1 1 } 5 y 0 } 2 1 2 2 x 5 log 1.1 1 } 5 y 0 } 2 1 2 x 5 2 log 1.1 1 } 5 y 0 } 2 1 2 5 2 log 1.1 1 } 50 y 2 y } 2 5 log 1.1 1 } 50 y 2 y } 2 Interchange x and y: y 5 log 1.1 1 } 50 x 2 x } 2 f 2 1 ( x ) 5 log 1.1 1 } 50 x 2 x } 2 Verify. ( f + f 2 1 )( x ) 5 f 1 log 1.1 1 } 50 x 2 x } 22 5 5 5 5 } x 1 ( 5 5 0 0 x 2 x ) } 5 } 5 5 0 0 x } 5 x ( f 2 1 + f )( x ) 5 f 2 1 1 } 1 1 5 1 0 .1 2 x } 2 5 log 1.1 1 2 5 log 1.1 1 2 5 log 1.1 1 } 1.1 1 2 x } 2 5 log 1.1 (1.1 x ) 5 x 45. (a) f ( f ( x )) 5 ˇ 1 w 2 w ( w f ( w x ) w ) 2 w 5 ˇ 1 w 2 w ( w 1 w 2 w x w 2 ) w 5 ˇ x 2 w 5 ) x ) 5 x , since x \$ 0 (b) f ( f ( x )) 5 f 1 } 1 x } 2 5 } 1 1 / x } 5 x for all x 0 46. (a) Amount 5 8 1 } 1 2 } 2 t /12 (b) 8 1 } 1 2 } 2 t /12 5 1 1 } 1 2 } 2 t /12 5 } 1 8 } 1 } 1 2 } 2 t /12 5 1 } 1 2 } 2 3 } 1 t 2 } 5 3 t 5 36 There will be 1 gram remaining after 36 hours. 47. 500(1.0475) t 5 1000 1.0475 t 5 2 ln(1.0475 t ) 5 ln 2 t ln 1.0475 5 ln 2 t 5 } ln 1 ln .0 2 475 } < 14.936 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 5 1,000,000 1.0225 t 5 } 8 3 } ln(1.0225 t ) 5 ln 1 } 8 3 } 2 t ln 1.0225 5 ln 1 } 8 3 } 2 t 5 } ln ln 1 ( . 8 0 / 2 3 2 ) 5 } < 44.081 It will take about 44.081 years. 49. (a) y 5 2 2539.852 1 636.896 ln x (b) When x 5 75, y < 209.94. About 209.94 million metric tons were produced.
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