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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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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