Suppose that there is a large jar of candy upon a shelf. You cannot
see into the jar nor can you differentiate between candy bars by feel.
In the jar there are 10 Mars Bars, 6 Almond Joy, and 4 Mounds.
1. If you draw 2 candy bars from the jar, what is the
Math 160-004
Exam 1 7L
7 February 2012 Name: 54 l W ‘ 2A5
Read all directions carefully. Write legibly, with correct mathematical notation, and clearly indicate
ﬁnal answers. Show all work for full credit. Make sure you attempt them all and explain your
Math 160
Synopsis of Section 4-1
8 February 2012
The compound interest formula is given by
Pt = P0 1 +
r
n
nt
Pt is the principal amount at time t, P0 is the initial principal, r is the annual rate (as a decimal,
and typically an annual rate), and n is ho
Math 160
Quiz 5-1 55/14» lam;
Please refer to the following ﬁgure for exercises 1 and 2.
The ﬁgure approximates the rate of change of the price of eggs over a 70—month period, where E(t)
is the price of a dozen eggs (in dollars) and t is time (in months
Math 160
Synopsis of Section 4-2
10 February 2012
1
Exponential functions
An exponential function is one of the form
f (x) = bx
where b, called the exponential base, is a positive real number. A special case of this is
f (x) = ex
where is the e is a speci
Math 160
Synopsis of Section 4-4
14 February 2012
In section 4-4 we were introduced to the Chain Rule. The Chain Rule states that
If f (x) = g(h(x) then f (x) = h (x)g (h(x).
In less symbolic terms, the Chain Rule is: the derivative of the composition of
Math 160
Synopsis of Section 4-6
22 February 2012
Section 4-6 dealt with related rates. Recall the technique of implicit dierentiation from section
4-5. In that section we treated y as a function of x and then used the chain rule to take derivative.
In th
Math 160
Synopsis of Section 4-3
13 February 2012
In section 4-3 we covered the Product Rule and the Quotient Rule. The Product Rule states that
If f (x) = g(x)h(x), then f (x) = g (x)h(x) + g(x)h (x).
In less symbolic terms, the Product Rule is: the deri
Math 160
Exam 2
2 March 2012 Name: fa IM- +\‘OI\ 5
Read all directions carefully. Write legibly, with correct mathematical notation, and clearly indicate
ﬁnal answers. Show all work for full credit. Make sure you attempt them all and explain your
thinki
Math 160
Synopsis of Section 4-5
15/16 February 2012
In section 4-5 were were introduced to implicit dierentiation. It is not always possible to solve an
equation for one variable explicitly in terms of another variable. For instance x2 + y 2 = 9 is the
e
Math 160
Synopsis of Section 4-7
28 February 2012
Section 4-7 dealt with elasticity of demand. If the x = f (p) gives demand, x, as a function of price,
p, then the elasticity of demand is given by the formula
E(p) =
pf (p)
.
f (p)
If E(p) > 1 then we sa
Math 160
Exam 3
21 March 2012
Name: Solutions
Read all directions carefully. Write legibly, with correct mathematical notation, label all units when
applicable, and clearly indicate nal answers. Show all work for full credit. Make sure you attempt them al
207ers,
Here is my work for 2 of the suggested problems:
9-12
H0: > $31,912
= 0.05
t calc=
HA: < $31,912
X
n = 12
calc
= 31,258.08 s = 4,199.8
31258.0831912
4199.8
12
= -0.5394
Pcalc = P(t < -0.54)
= 0.25 0.35
X
= -1.7959 =
crit
X31912
4199.8
12
= 29734
1. In a deck of American playing cards there are 4 aces and 16 face
cards. From a complete deck of 52 cards, what is the chance that the first
2 cards will result in a Blackjack (a combination of an ace and a face
card)?
52*51=2652 4*16=64 16*4=64
p(BJ)=
Math 160
Quiz 5-2
Solutions
Refer to the following graph of the function S for questions 1 thru 9.
S(x)
b
e
h
i
x
a
c
d
f
g
j
1. The graph of S is concave upward on the intervals (a, b), (d, e), (g, h), (h, i), and (i, j).
2. The graph of S is concave dow
Math 160
Quiz 6-1 and 6-2
PART A: Find the particular antiderivative of the derivative that satises the given condition.
dy
= 3x1 + x2 and y(1) = 1
dx
a) y = 3 ln |x|
1
+2
x
b) y = 3 ln |x|
1
1
x
c) y = 3 ln |x| +
1
x
d) y = 3 ln x
1
+2
x
e) y = 3 ln x
Math 160
Quiz 5-5 and 5-6
1 Find the absolute maximum and minimum, if either exists, for the function f (x) =
Note: This is like exercises 17-32 of section 5-5.
8x
.
x2 + 4
2 Find the absolute maximum and minimum if either exists on the indicated interval
Math 160
Quiz 6-3
PART A: Find the particular or general solution for each dierential equation.
1.
dy
= 20x2
dx
y(5) = 0
40
8
+
3
x
25
20
y = 4
x
20
y=
4
x
20
+4
y=
x
20
y = +4
x
The solution is not listed.
a) y =
b)
c)
d)
e)
f)
2.
dy
= x2 4x
dx
a) y = x
Math 160
Synopsis of Chapter 5
Interpreting the rst and second derivative of functions
Let f be a function. Intervals on which f (x) > 0 correspond to intervals on which f is increasing.
Intervals on which f (x) < 0 correspond to intervals on which f is d