PREVIEW Version HW 13 homan (57225)
This print-out should have 14 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
CalC7c44b
001 (part 1 of 3) 10.0 points
1
4. cooking time = 46 minutes
5. cooking time = 56 minutes
003 (part 3 of 3) 10.0 points
Jane wishes to bake an apple pie for dessert. (iii) What was the initial temperature of the
pie?
The baking instructions say that she should
bake the pie in an oven at a constant temperature of 230 C . Being a mathematician, she
1. initial temp = 49 C
knows that the temperature T of the pie after
t minutes of baking will be given by
2. initial temp = 47 C
T (t) = 230 Aekt ,
where A and k are constants. After 17 minutes of baking she notices that the temperature of the pie is 138 C , while after 34 minutes
it is 184 C .
(i) Determine the constants A and k .
1. T (t) = (230 184 2t/34 ) C
2. T (t) = (230 184 2t/17 ) C correct
3. T (t) = (230 92 2t/34 ) C
4. T (t) = (230 184 2t/17 ) C
5. T (t) = (230 92 4t/17 ) C
002 (part 2 of 3) 10.0 points
(ii) If the pie is cooked when it reaches a temperature of 207 C , how long does it have to
be in the oven?
1. cooking time = 61 minutes
2. cooking time = 41 minutes
3. cooking time = 51 minutes correct
3. initial temp = 46 C correct
4. initial temp = 50 C
5. initial temp = 48 C
CalC7c47a
004 10.0 points
If the half-life of a certain radioactive substance is 1400 years, estimate how many years
must elapse before only 15% of the radioactive
substance remains.
1. # years 3830 correct
2. # years 3930
3. # years 4130
4. # years 4230
5. # years 4030
CalC7c49a
005 10.0 points
An archeologist nds a skull in Piltdown
Park in England. He discovers that only 1%
Version PREVIEW HW 13 homan (57225)
of the original amount of carbon-14 is still
present in the skull. If the decay constant for
carbon-14 is 19 105 , estimate the age of the
skull.
1. age skull 23900 years
5
4.
6
correct
5.
4
3.
2. age skull 24200 years correct
CalC7e12a
008 10.0 points
3. age skull 24100 years
4. age skull 24400 years
5. age skull 24000 years
CalC7e01a
006 points
Find 10.0 the value of f (1) when
f (x) = 3 sin1 x + 6 tan1 x .
1. f (1) = 4
2. f (1) = 2
3. f (1) =
Simplify the expression
f (x) = tan sin1 x .
1. f (x) =
1 + x2
2. f (x) =
1 x2
1
1 x2
x
4. f (x) =
1 + x2
3. f (x) =
1
1 + x2
x
correct
6. f (x) =
1 x2
5. f (x) =
7
2
4. f (1) = 3 correct
5. f (1) =
2
5
2
CalC7e22b
009 10.0 points
Find the derivative of f when
CalC7e03s
007 10.0 points
Find the exact value of
sin1
.
in the interval 0,
2
1.
7
2.
3
2
2
f ( x) =
1. f (x) = cos
2. f (x) =
3. f (x) =
4. f (x) =
1
x
sin1
2
3
2
.
x
x
sin
3
3
x
1
sin1 correct
3
9 x2
x
2
sin1
3
1 9 x2
x
x
1
cos sin
2
3
3
Version PREVIEW HW 13 homan (57225)
5. f (x) =
6. f (x) =
x
2
sin1
3
9 x2
1
x
sin1
2
3
1 9x
CalC7e25a
010 10.0 points
f (x) = tan1
x
.
6 x2
f (x) = 2 sin1
1
correct
6 x2
6
5. f (x) =
6 x2
CalC7e34a
011 10.0 points
Find the derivative of f when
1
2x
1
2+x
2+x
2x
2x
correct
2+x
x
6. f (x) =
4 x2
2 5 + x2 .
CalC7e44a
013 10.0 points
Find the derivative of
x
f (x) = sin tan1
3
(Hint: rst simplify f .)
1. f (x) =
1. f (x) =
5+x
correct
25 + x2
2. f (x) =
2. f (x) =
5x
25 + x2
3. f (x) =
6
(x2 + 3)1/2
( x2
1
+ 3)1/2
( x2
3
correct
+ 3)3/2
5+x
25 + x2
4. f (x) =
6
(x2 + 3)3/2
5
4. f (x) =
25 + x2
5. f (x) =
1
(x2 + 3)3/2
x
25 + x2
6. f (x) =
3. f (x) =
5. f (x) =
4 x2 .
5. f (x) =
4. f (x) =
x
+ ln
5
2. f (x) =
x
+
2
2
4 x2
4. f (x) =
x
+6
6
2. f (x) =
6 + x2
x
3. f (x) =
26
x
x2
f (x) = tan1
Find the derivative of f when
3. f (x) =
(Hint : rst simplify f .)
1. f (x) =
CalC7e34e
012 10.0 points
1. f (x) =
Determine f (x) when
3
( x2
3
+ 3)1/2
.
Version PREVIEW HW 13 homan (57225)
CalC7c50a
014 10.0 points
The amount, $A, in a Wells Fargo savings
account satises the dierential equation
dA
= 0.08 A.
dt
Katy deposits $100 in such a savings account.
Find out how much money will be in her
account after 4 years, leaving the answer in
exponential form.
1. A(4) = $100 e3.2
2. A(4) = $100 e3.2
3. A(4) = $100 e0.32
4. A(4) = $100 e0.32 correct
5. A(4) = $100 e32
4