Version PREVIEW – HW 13 – hoffman – (57225)
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CalC7c44b
001
(part 1 of 3) 10.0 points
Jane wishes to bake an apple pie for dessert.
The baking instructions say that she should
bake the pie in an oven at a constant temper
ature of 160
◦
C
. Being a mathematician, she
knows that the temperature
T
of the pie after
t
minutes of baking will be given by
T
(
t
) = 160

Ae
−
kt
,
where
A
and
k
are constants. After 14 min
utes of baking she notices that the tempera
ture of the pie is 96
◦
C
, while after 28 minutes
it is 128
◦
C
.
(i) Determine the constants
A
and
k
.
1.
T
(
t
) = (160

128
·
2
−
t/
14
)
◦
C
correct
2.
T
(
t
) = (160

64
·
4
−
t/
14
)
◦
C
3.
T
(
t
) = (160

128
·
2
t/
14
)
◦
C
4.
T
(
t
) = (160

64
·
2
−
t/
28
)
◦
C
5.
T
(
t
) = (160

128
·
2
−
t/
28
)
◦
C
Explanation:
Jane’s observations tell us that
T
(14) = 96 = 160

Ae
−
14
k
,
T
(28) = 128 = 160

Ae
−
28
k
,
i.e.
,
Ae
−
14
k
= 64
,
Ae
−
28
k
= 32
.
Thus
e
14
k
= 2 and
A
= 128. Consequently,
T
(
t
) = 160

128
·
2
−
t/
14
.
002
(part 2 of 3) 10.0 points
(ii) If the pie is cooked when it reaches a tem
perature of 144
◦
C
, how long does it have to
be in the oven?
1.
cooking time = 42 minutes
correct
2.
cooking time = 47 minutes
3.
cooking time = 37 minutes
4.
cooking time = 32 minutes
5.
cooking time = 52 minutes
Explanation:
The length of time
t
0
the pie needs to be in
the oven is given by
T
(
t
0
) = 144 = 160

128
·
2
−
t
0
/
14
.
Thus 2
t
0
/
14
= 8. Solving for
t
0
we see that
cooking time = 42 minutes.
003
(part 3 of 3) 10.0 points
(iii) What was the initial temperature of the
pie?
1.
initial temp = 35
◦
C
2.
initial temp = 32
◦
C
correct
3.
initial temp = 33
◦
C
4.
initial temp = 36
◦
C
5.
initial temp = 34
◦
C
Explanation:
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Version PREVIEW – HW 13 – hoffman – (57225)
2
The initial temperature,
T
(0), of the pie is
given by
initial temp = 32
◦
C
.
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 Spring '11
 Cathy
 Calculus, Derivative, tan θ

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