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
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
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 (a
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 pric
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 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, t
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
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)
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.
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
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 th
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
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)
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 a
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
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)
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
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 l
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