9.
Q
(
t
)
5
200(30
2
t
)
2
5
200(900
2
60
t
1
t
2
)
5
180,000
2
12,000
t
1
200
t
2
Q
9
(
t
)
5 2
12,000
1
400
t
The rate of change of the amount of water in the tank after
10 minutes is
Q
9
(10)
5 2
8000 gallons per minute.
Note that Q
9
(10)
,
0, so the rate at which the water is
running
out
is positive. The water is running out at the rate
of 8000 gallons per minute.
The average rate for the first 10 minutes is
}
Q
(1
1
0
0
)
2
2
Q
0
(0)
}
5
}
80,000
2
10
180,000
}
5 2
10,000 gallons per
minute.
The water is flowing out at an average rate of 10,000
gallons per minute over the first 10 min.
10. (a)
Average cost
5
}
c
(
1
1
0
0
0
0)
}
5
}
11
1
,
0
0
0
00
}
5
$110 per machine
(b)
c
9
(
x
)
5
100
2
0.2
x
Marginal cost
5
c
9
(100)
5
$80 per machine
(c)
Actual cost of 101st machine is
c
(101)
2
c
(100)
5
$79.90, which is very close to the
marginal cost calculated in part (b).
11. (a)
[0, 50] by [
2
500, 2200]
The values of
x
which make sense are the whole
numbers,
x
$
0.
(b)
Marginal revenue
5
r
9
(
x
)
5
}
d
d
x
}
3
2000
1
1
2
}
x
1
1
1
}
24
5
}
d
d
x
}
1
2000
2
}
x
20
1
00
1
}
2
5
0
2
5
}
(
x
2
1
00
1
0
)
2
}
(c)
r
9
(5)
5
}
(5
2
1
00
1
0
)
2
}
5
}
20
3
0
6
0
}
<
55.56
The increase in revenue is approximately $55.56.
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 Fall '08
 GERMAN
 Rate Of Change, Marginal concepts, average rate, maximum possible profit, little extra revenue

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