(b)
The given graph is reflected about the
x
-axis.
(c)
The given graph is shifted left 1 unit, stretched
vertically by a factor of 2, reflected about the
x
-axis,
and then shifted upward 1 unit.
(d)
The given graph is shifted right 2 units, stretched
vertically by a factor of 3, and then shifted downward
2 units.
61. (a)
(b)
62. (a)
V
5
100,000
2
10,000
x,
0
#
x
#
10
(b)
V
5
55,000
100,000
2
10,000
x
5
55,000
2
10,000
x
52
45,000
x
5
4.5
The value is $55,000 after 4.5 years.
63. (a)
f
(0)
5
90 units
(b)
f
(2)
5
90
2
52 ln 3
<
32.8722 units
(c)
[0, 4] by [
2
20, 100]
64.
1500(1.08)
t
5
5000
1.08
t
5 }
5
1
0
5
0
0
0
0
} 5 }
1
3
0
}
ln (1.08)
t
5
ln
}
1
3
0
}
t
ln 1.08
5
ln
}
1
3
0
}
t
5
}
ln
ln
(1
1
0
.0
/
8
3)
}
t
<
15.6439
It will take about 15.6439 years. (If the bank only pays
interest at the end of the year, it will take 16 years.)
65. (a)
N
(
t
)
5
4
?
2
t
(b)
4 days: 4
?
2
4
5
64 guppies
1 week: 4
?
2
7
5
512 guppies
(c)
N
(
t
)
5
2000
4
?
2
t
5
2000
2
t
5
500
ln 2
t
5
ln 500
t
ln 2
5
ln 500
t
5 }
ln
ln
50
2
0
}
<
8.9658
There will be 2000 guppies after 8.9658 days, or after
nearly 9 days.
(d)
Because it suggests the number of guppies will
continue to double indefinitely and become arbitrarily
large, which is impossible due to the finite size of the
tank and the oxygen supply in the water.
66. (a)
y
5
20.627
x
1
338.622
[0, 30] by [
2
100, 1000]
(b)
When
x
5
30,
y
<
957.445. According to the
regression equation, about 957 degrees will be earned.
(c)
The slope is 20.627. It represents the approximate
annual increase in the number of doctorates earned by
Hispanic Americans per year.
67. (a)
y
5
14.60175
?
1.00232
x
(b)
Solving
y
5
25 graphically, we obtain
x
<
232.
According to the regression equation, the population
will reach 25 million in the year 2132.
(c)
0.232%
y
x
3
–3
–3
3
(–3, –2)
(–1, 1)
(1, –1)
(3, 2)
y
x
3
3
–3
–3
(–3, 2)
(–1, –1) (1, –1)
(3, 2)
y
x
4
–2
4
(–1, –2)
(2, 4)
(3, –2)
y
= 3
f
(
x
– 2) – 2
y
x
3
2
–4
(–4, 1)
(–1, –3)
(0, 1)
y
= –2
f
(
x
+ 1) + 1
y
x
3
–3
–3
3
(–3, 0)
(0, –2)
(1, 0)
y
= –
f
(
x
)
Chapter 1 Review
41