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[1] Preparation for Business Students
(This article consists of the college algebra portions of the Report from the
Business and Management workshop held as part of the CRAFTY Curriculum
Foundations Project. The workshop included thirty six participants from
Business and six mathematicians. The full report, written by Chris
Lamoureux---Head, Finance Department, Arizona University, is available in the
MAA publication: Curriculum Foundations Project, Voices of the Partner
Disciplines)
College algebra programs can help prepare students going into business by
stressing problem solving using business applications, conceptual
understanding, quantitative reasoning, and communication skills.
In general, business faculty are less concerned with specific course content
than with developing quantitative literacy and analytical ability in students.
A measure of the curriculum's success is the students' comfort level when
exposed to a new formula in a business class. When in doubt, mathematics
faculty should cover less material---and treat the material with
respect---imparting to students a sense of importance of mathematics as a
necessary part in the development of successful business people.
Business decisions are most commonly made under conditions of uncertainty and
risk. Inferences must be drawn from data and information that are incomplete,
inconclusive, and most likely imprecise. Whenever possible, math courses
should attempt to illustrate this ambiguity and provide guidance in dealing
with uncertainty and variation. Business faculty recommend that mathematics curriculums include:
Algebra is a basic prerequisite to study business. Students should be able to
solve simultaneous equations, understand the concept of function and
functional relationships, understand the use of common functions in modeling
business concepts, construct and understand graphs, and use abstraction to
build simple models.
Students should work on group projects or assignments, and be asked to prepare
written reports and oral presentations to communicate the results of their
analysis. The ability to work effectively in groups and the ability to explain
quantitative concepts and results in plain English are highly valued skills in
business. [2] Indexes
The Consumer Price Index (CPI) is often referenced in social and political
discussions as well as in economic discussions. For example, CPI is used in
measuring inflation and a central question in the debate over reforming social
security is whether future increases in benefits should be tied to changes in
wages or to changes in the CPI. Because our economy is consumer based,
learning about CPI should be part of every person's education. Since the
computations only involve working with fractions and manipulating an
elementary equation, CPI, or indexes in general, is a very suitable topic for
a Contemporary College Algebra class. The Web and beginning college economics
texts serve as resources for both students and instructors. In addition,
including two or three classes on CPI provides a nice opportunity to invite an
economics or business instructor to speak to the class. This would enhance the
connection between business and mathematics at both the student and faculty
levels.
How much does a gallon of gas today, cost in 1970 dollars? The first Ford car
produced, a 2-person runabout, sold for $850 in 1903. How does this price,
expressed in today's dollars, compare with the price of a new Ford coupe
today? How can the values of the same economic variable from two different
time periods be compared? In order to answer these types of questions, one
needs to establish a base price and then make comparisons relative to this
base. That is the concept of an Index. A price index measures the
price level at a given period relative to a chosen base period.
Index Number =
Example. A first-class postage stamp cost 6 cents in 1970. Using 1970 as the
base period, what is today's first-class postage index?
First-Class Postage Index =
Thus it costs 6.17 times as much to buy a first-class postage stamp today as
it did in 1970. Because the index number for the base period is always 100
(Why?), the index of 617 indicates a 517 percent increase in the cost of a
first-class postage stamp since 1970. Note that
percent change = price index number - 100
The CPI represents the change in price of a representative set (i.e., a
``market basket'') of goods and services commonly purchased by households
(e.g., food, soap, paper towels, energy, automobiles, haircuts, etc.). The
base period, say 1967, is denoted by writing ``(1967=100).''
Knowing the sequence of yearly CPI numbers enables one to compare prices in
different periods by manipulating the previous Index Number equation. For
example, what is $1,000 today worth in 1980 dollars? (The reader should fill
in the explanations for the following list of manipulations.)
Index 1980 =
Cost 1980=(Index 1980)(Base Yr. Cost)/100
Cost 2005=(Index 2005)(Base Yr. Cost)/100
Cost 1980 = Cost 2005 x
Thus if the 1980 Index is 450 and the 2005 Index is 900, $1,000 in 2005 would
have been worth $500 in 1980.
Given the following list of CPI numbers (1982-84 = 100), determine how much $1
in 1913 would be worth today. Also explain what might have caused the index
numbers to decrease from 1925 through 1933. (The 2005 number is an estimate.)
The complete list from 1913 is available at www.CPI.org.
There are many indexes. The Gross Domestic Product (GDP) measures changes in
the total output of our national economy. Samples of more specialized indexes
include Consumer Confidence Index, Import Price Index, NASA New Start Index,
and Produce Price Index. [3] Problems of the Week
Miami Dade College
The following problems were selected from the ``Problem of the Week'' program
run by the mathematics department at Miami Dade College.
1. Three different numbers are chosen such that when each of the numbers is
added to the average of the other two, the results are 65, 69, and 76,
respectively. Find the average of the original three numbers.
2. Suppose all the vehicles traveling on a certain interstate highway have
either 18 wheels on five axles or four wheels on two axles. In a five-minute
period, 224 wheels on 88 axles passed by an observation station. How many
vehicles passed by the observation station during that period?
3. The area of the top of a box is 30 sq. in. and the area of the front is 12
sq. in. If the surface area of the box is 164 sq. in., what is the volume of
the box?
4. Two ladders, one of which is twice as long as the other, rest on the floor
and reach the same vertical height on a wall. The shorter ladder makes an
angle of 60 degrees with the floor. Determine the sine of the angle that the
longest ladder makes with the floor.
5. In the base 10 number system, the number 526 means
[4] Capacity versus Wing Span
The March issue of Continental Airlines in-flight magazine contained the
following table listing the different types of airplanes in their fleet, the
capacity of each, and the wingspan of each.
Plot the data of Capacity vs. Wing Span and then fit a curve to your scatter
plot.
What does your model predict for the length of the wing span for a plane that
holds 75 passengers?
Interpret the meaning of the y-intercept of your model.
Interpret the meaning of the slope of your model.
How do you explain the strange behavior of the middle two points in the
scatter plot?
[5] Notices
* Supported by the National Science Foundation and the U.S. Military Academy. |
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