Chapter 5: Urban Econ Growth
Normally, growth is measured in terms of per capita income, local GDP, etc.
Most of these measures, e.g., GDP, are the product of price and quantity
That is, growth may be driven by P or by Q.
To avoid the problem that growth
CHAPTER 3, Part 2, Lecture Notes
II. COSTS IN CLUSTERS
in general: there are conflicting cost trends in clusters

labor cost is normally higher in clusters

other costs might fall
III. LOCALIZATION ECONOMI
Assume an adult dose of A = 375 mg, so that Cowlings rule and Friend's rule become
functions of the childs age N. Sketch the graphs of these two functions.
A)
B)
90
C
80
70
60
50
40
30
20
10
0.5 1 1.5 2 2.5 3 3.5 4
N
68)
f (t) =
t2
1
; 2 t t8
4
A) min
C)
68)
2
1
=  ; max = 5
9
min = 
1
; max = 32
132
B) min
2
1
=  ; max = 5
132
D) min
2
=  ; max = 32
5
Answer: B
69)
1
;x0
x + 12
f (x) =
A) no
C)
69)
min or max
B) no
no min; max = 12
D) min
Answer: B
39
min; max
84)
84)
y
b
c
a
x
A)
lim
f (x) = b
xa
B) The
C)
lim
f (x) = c
xa
D)
limit fails to exist.
lim
f (x) = a
xa
Answer: B
85)
85)
y
b
a
x
A) a
C)
B) b
0
D) The
limit fails to exist.
Answer: B
Find the indicated limit if exists.
lim 5
86)
(x + 5x4 + 2)
x0
A) Th
3)
a. (23  32 )15/13
A) a.
b.
1
b. (2162/3 + 5122/3)3/2
3)
B) a.
1
1
b.
728
1
1000
C)
a. undefined
1
b.
728
D) a.
undefined
1
b.
1000
Answer: A
Use the properties of exponents to simplify the given expressions.
3 1/3
4) (8x2 y )
2/3
A) 2x y
B)
8 2/3
x
120)
When the price of a certain commodity is p dollars per unit, the manufacturer is willing
to supply x hundred units, where
120)
3p2  x2 = 12
How fast is the supply changing when the price is $4 per unit and is increasing at the rate
of 82 cents per m
39) A
payasyougo cell phone company offers a monthly plan for $29 that includes 150
minutes of calls. After that, calls are an additional 7 cents per minute up to a maximum
of 1200 minutes. Let C(m) be the cost in dollars of making m minutes of calls w
21) According
to the Ebbinghaus model, the fraction F(t) of subject matter you will
remember from this course t months after the final exam can be estimated by the formula
21)
F(t) = B + (1  B)ekt
where B is the fraction of the material you will never f
Solve the problem.
10) Fill in the missing interpretations in the table using the example as a guide.
then
f (t0 + h ) f (t0 )
h
lim f (t0 + h ) f (t0 )
h0
h
If f (t) represents.
represents.and
represents.
The average rate of The instantaneous
The numbe
67)
y=
A)
4
; u = x2
u6
8x
(x  6)2
67)
B)
2
4x
(x  6)2
C)
8x
(x  6)2
D)
4x
(x  6)2
2
Answer: A
Use the chain rule to compute the derivative
68)
dy
for the given value of x.
dx
y = 3u4 + 4u + 4; u = x3 + 3x  4 for x = 1
A) 24
C) 12
68)
24
B)
D) 4
75) An
art gallery offers 30 prints by a famous artist. If each print in the limited edition is
priced at p dollars, it is expected that q = 540  2p prints will be sold.
75)
a. Find the elasticity of demand. Determine the values of p for which the demand
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solve the problem.
96) A business manager determines that t months after production begins on a new product,
the number of units produced will be P thousand, where
96
33) Vickis
company can produce digital recorders at a cost of $25 apiece. It is estimated
that if the recorders are sold for p dollars apiece, consumers will buy 95  p of them a
month. The graph of Vickis monthly profit as a quadratic is shown below. Est
37) A
manufacturer of motorcycles estimates that if x thousand dollars is spent on
advertising, then
M(x) = 2500 +
145 523
 2
x
x
37)
3 x 18
cycles will be sold. At what rate will sales be changing when $9000 is spent on
advertising? Are sales increasing
104)
104)
A 5year projection of population trends suggests that t years from now, the population
3
2
of a certain community will be P(t) = t + 10t + 53t + 220 thousand. The rate of change
of population, R(t) = P'(t).
a. At what rate does the population
Solve the problem.
52) A manufacturers total cost consists of a fixed overhead of $4000 plus production costs
of $30 per unit. Express the total cost as a function of the number of units produced, and
sketch its graph.
A) y = C(x) = 30x + 4000
B) y = C(x
A) P(x)
=
1.21x
if x 60,000
1.07x + 8400 if x > 60,000
100,000
80,000
60,000
40,000
20,000
40000
B) P(x)
=
80000
1.21x
if x 60,000
1.07x + 12,600 if x > 60,000
100,000
80,000
60,000
40,000
20,000
40000
C)
P(x) =
80000
1.21x
if x 60,000
1.07x + 8400 if x >
57) A
certain stock had an initial public offering (IPO) price of $15 per share and is traded
24 hours a day. Sketch the graph of the share price over a 2year period for the following
case:
The price takes just 4 months to rise at a constant rate to $25
61) Each
ounce of Food I contains 4 g of carbohydrate and 3 g of protein, and each ounce of
Food II contains 3 g of carbohydrate and 5 g of protein. Suppose x ounces of Food I are
mixed with y ounces of Food II. The foods are combined to produce a blend t
89) The
growth of certain insects varies with temperature. Suppose a particular species of
insect grows in such a way that the volume of an individual is
V(T) = 0.42(0.02T2 + 0.5T + 3.56) cm3
when the temperature is TC, and that its mass is m grams, wher
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
121)
The accompanying graph shows the number of units in inventory at a certain
business over a 2year period. When is the graph discontinuous? What do you
think is happen
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Answer: D
Find the intervals of increase and decrease for the given function.
4) f (x) = x2 + 4x + 3
A) f (x) is increasing for x < 2; f (x) is decreasing for x > 2.
B) f (x) is increasing for 3 < x < 1; f (x) is decreasing
83) Find
two positive numbers whose sum is 98 and whose product is as large as possible.
A) x = 44, y = 54
B) x = 1, y = 97
C) x = 49, y = 49
D) x = 7 2, y = 7 2
83)
Answer: C
84) A
city recreation department plans to build a rectangular playground having
52)
y=
A)
2x  5
; x = 2
3x + 1 0
13
49
52)
B) 
2
3
C)

13
49
D) 
13
7
Answer: C
6ROYHWKHSUREOHP
53) Find h (2) if h(x) = (x2  6)g(x) where g(2) = 3 and g (2) = 4.
A) 22
B) 20
C) 10
53)
D) 4
Answer: B
x3 + xg(x)
54) Find h (2) if h(x) =
wher
A) Drawing
a tangent line at each of the indicated points on the curve shows the
population is growing at approximately 9.6/day after 24 days and 2.4/day after 48
days. The tangent line slope is steepest at approximately 30 days.
B) Drawing a tangent line
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Answer: C
56) Sign
of f '(x)


56)
1
Sign of f '(x)

+
1
31
A)
B)
5 y
5 y
4
4
3
3
2
2
1
1
5 4 3 2 1
1
1
2
3
4
5x
5 4 3 2 1
1
2
2
3
3
4
4
5
5
C)
1
2
3
4
5x
1
2
3
4
5x
D)
5 y
5 y
4
4
3
3
2
2
1
1
5 4 3