This preview shows pages 1–4. Sign up to view the full content.
JL1
8/03
1
1.
Find a formula for the area of a circular ring whose inner radius is
r
and whose outer radius is
r
+
1 (Figure 1).
This is a LINEAR FUNCTION because its graph is a straight line.
Sketch its
graph in an
rA
plane
Figure 1
2.
(a)
Give approximate values of
A
(1) and
A
(4) for the function
A
(
x
) of Figure 2.
(b)
Find the
approximate solutions
x
of
A
(
x
) = 40 and of
A
(
x
) = 60 with 0
≤
x
≤
6.
(c)
Which is greater
[
A
(2)]
2
or
A
(2
2
)?
Explain.
Figure 2
3.
The symbols
A
(2) have one meaning if
A
(
x
) is a function of
x
and another if A represents a
constant.
Explain.
4.
What are
p
(1),
p
(2), and
p
(3) if the points (1, 18), (2 –6), and (3,
) are on the graph of
p
?
5.
Figure 3 shows the graph of the velocity
v
(t) of a woman’s car
t
seconds after she leaves a parking
space.
She stops at a traffic light and then goes on the freeway.
Give approximate answers to the
following questions:
(a)
How long does she wait at the light?
(b)
The speed limit is 55 miles per
hour, and her trip is interrupted when she is stopped and given a speeding ticket.
When do you
imagine she sees the highway patrolman who stopped her?
(c)
During what time interval does she
exceed the speed limit on the freeway?
(d)
During part of the short drive between the parking
space and the traffic light, she drives at a constant speed.
What is it?
How far does she travel
during that time?
(Remember that an hour consists of 60
x
60 = 3600 seconds.)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document JL1
8/03
2
Figure 3
JL1
8/03
3
6.
The next table gives the number of registered political action committees (PAC’s) and the amounts
they contributed to candidates for the U. S. Congress during the campaigns for the 1974 through
1988 elections.
The contributions have been rounded to the nearest thousand dollars.
(a)
What
were the least and greatest increases in the number of PAC’s from one election to the next during
these years?
(b)
What were the least and greatest increases in the amounts contributed by PAC’s?
(c)
What was the average amount contributed per PAC in 1974?
In 1988?
POLITICAL ACTION COMMITTEES, 1974  1988
Year
1974
1976
1978
1980
1982
1984
1986
1988
Number of PAC’s
608
1146
1653
2551
3371
4009
4157
4268
Total contributions
(million dollars)
12.527
22.572
34.121
55.217
86.620
105.330
132.671
147.898
7.
A function
Q
has the values
Q
(5) = 7 and
Q
(10) = 21.
What are
(a)
10
Q
(10),
(b)
Q
(6 + 3 + 1),
(c)
Q
(100/20),
(d)
Q
(10)/
Q
(5), and
Q
(
Q
(5) + 3))?
8.
The average number of cigarettes
C
(
t
) smoked per person in the United States is given below for
1945 and every sixth year until 1987.
(a)
What are the change and relative change of
C
(
t
) from
1945 to 1963?
(b)
What are the change and relative change of
C
(
t
) from 1963 to 1987?
(c)
C
(
t
)
has been defined for all
t
between 1945 and 1987 in Figure 4 by joining the points given in the
table with line segments.
Find
C
(1953).
This is the average number of cigarettes smoked per
capita in 1953 according to the mathematical model in Figure 4.
In fact, the average that year
was 3500 cigarettes per person.
What error is made by using
C
(1953)?
What is the relative error
(the error divided by the correct value)?
(d)
In Figure 4 the numbers on the vertical axis run
from 3000 to 4500.
Figure 5 shows the same graph with all of the vertical axis shown from 0 to
4500.
Both graphs give good representations of changes in
C
(
t
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/18/2011 for the course MAC 2311 taught by Professor Jameslang during the Fall '11 term at Valencia.
 Fall '11
 JamesLang
 Calculus

Click to edit the document details