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41. (a)
Regression equation
y
5
}
1
1
2
1
7
7
0
.2
1
8
.7
e
3
2
0.36
x
}
[0, 20] by [
2
300, 2800]
(b)
Note that
y
95 }
d
d
x
}
2701.73(1
1
17.28
e
2
0.36
x
)
2
1
52
2701.73(1
1
17.28
e
2
0.36
x
)
2
2
(17.28)(
2
0.36
e
2
0.36
x
)
<
The graph of
y
9
is shown below.
[0, 20] by [
2
75, 275]
Using graphing techniques,
y
9
has its maximum at
x
<
7.92. This corresponds to the year 1998 and
represents the inflection point of the logistic curve. The
logistic regression equation predicts that the rate of
increase in debit card transactions will begin to
decrease in 1998, and since
y
(7.92)
<
1351, there are
approximately 1351 million transactions that year.
(c)
As
x
increases, the value of
y
will increase toward
2701.73. The logistic regression equation predicts a
ceiling of approximately 2702 million transactions per
year.
42.
f
(
x
)
5
2 cos
x
2
ˇ
1
w
1
w
x
w
f
9
(
x
)
52
2 sin
x
2
}
2
ˇ
1
w
1
1
w
x
w
}
x
n
1
1
5
x
n
2 }
f
f
9
(
(
x
x
n
n
)
)
}
5
x
n
2
The graph of
y
5
f
(
x
) shows that
f
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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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