Pre-Calc Homework Solutions 31

Pre-Calc Homework Solutions 31 - Section 1.6 50. (a) y...

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50. (a) y 52 590.969 1 152.817 ln x (b) When x 5 85, y < 87.94. About 87.94 million metric tons were produced. (c) 2 590.969 1 152.817 ln x 5 120 152.817 ln x 5 710.969 ln x 5 } 7 1 1 5 0 2 . . 9 8 6 1 9 7 } x 5 e } 7 1 1 5 0 2 . . 9 8 6 1 9 7 } < 104.84 According to the regression equation, oil production will reach 120 million metric tons when x < 104.84, in about 2005. 51. (a) Suppose that f ( x 1 ) 5 f ( x 2 ). Then mx 1 1 b 5 mx 2 1 b so mx 1 5 mx 2 . Since m ± 0, this gives x 1 5 x 2 . (b) y 5 mx 1 b y 2 b 5 mx } y 2 m b } 5 x Interchange x and y . } x 2 m b } 5 y f 2 1 ( x ) 5 } x 2 m b } The slopes are reciprocals. (c) If the original functions both have slope m , each of the inverse functions will have slope } m 1 } . The graphs of the inverses will be parallel lines with nonzero slope. (d) If the original functions have slopes m and 2} m 1 } , respectively, then the inverse functions will have slopes } m 1 } and 2 m , respectively. Since each of } m 1 } and 2 m is the negative reciprocal of the other, the graphs of the
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