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Water
Consumption in United States
Comprehension
 What is the
main source of drinking water for your community?
 What are
other major uses for water in your community?
 What factors
could lead to an increase in the amount of water used each year?
 What factors
could lead to a decrease in the amount of water used each year?
 Where does
“used” water go?
 What are
some consequences of increased water usage?
Acquisition
Mathematical
Topics: Learn or review mathematical concepts and skills needed
to study trends in US water consumption. See the Review Topics.
Application
Apply mathematical
concepts and use appropriate technology to analyze past trends.
Information
The table below
provides information on U.S. water usage for selected years. The
table below lists only the amount of water (in billion gallons per
day) withdrawn for public supply, such as drinking water. (Water
used for irrigation, industrial use and power generation is not
included. These figures are also available in the Statistical Abstract.)
Year 
1960 
1965 
1970 
1975 
1980 
1985 
1990 
1995 
Withdrawal
for public supply (billion gallons) 
21 
24 
27 
29 
34 
38 
41 
43 
US Population
(million persons) 
180.7 
194.3 
205.1 
216.0 
227.7 
238.5 
250.0 
263.1 
Source: Statistical
Abstract of the United States, U.S. Census Bureau
Objectives
To
Determine:
 Trends for
water withdrawal;
 Trends for
U.S. population;
 Trends for
per capita withdrawal
Questions
How
much water do we use?
 We will write
a function that describes the annual rate of water withdrawal
with units billion gallons per year. To do this, assume that if
W billion gallons are withdrawn in one year then the rate is W
billion gallons per year. For convenience, let t denote years
since 2000; that is, t = 0 in 2000. Let W denote the rate of U.S.
water withdrawal (in billion gallons per year).
 Make
points out of the data and plot them; use a (t,W) coordinate
system.
 Use linear
regression to fit the data with a linear function. Then multiply
this function by 365 to get the annual withdrawal rate. Call
this function W(t) and graph it.
 For each
of the years you have data provided, compare the actual withdrawal
rate with the rate predicted by your function. Why do you
think the figures are different?
 Use the function
W(t) to answer these questions.
 Estimate
the withdrawal rate in 1993.
 Predict
the withdrawal rate for 2004.
 Predict
when the annual withdrawal rate will reach 20,000 billion
gallons per year.
 Use the function
W(t) and the Riemann Sum Applet to determine the amount of water
withdrawn in the U.S. from 1990 through 2000. Estimate the amount
of water withdrawn for each year by using the midpoint of the
interval for that year. For example, for 1990 the interval corresponds
to [10,9) and the approximate withdrawal rate is (W(9.5) billion
gallons per year) x (1 year).
 Next, use
the Riemann Sum Applet to find the total amount of water withdrawn
from the year 2000 through 2020.
 Estimate
when the total withdrawal since the year 2000 reaches 800 billion
gallons?
How
many people are using the water?
 Next we will
write a function that describes U.S. population. For this function,
Let P denote the U.S. population in millions and again t denotes
years since 2000; that is, t = 0 in 2000.
 Make
points out of the data and plot them; use a (t,P) coordinate
system.
 Use linear
regression to fit the data with a linear function. Call this
function P(t) and graph it.
 What
patterns do you see?
 Use the function
P(t) to answer these questions.
 Estimate
the population in 1993.
 Predict
the population for 2004.
 Predict
when the population will reach 300 million.
How
much water do we use per person?
 Per capita
water withdrawal rate means water withdrawal rate per person.
 According
to the data in the table, in 1990 the rate of water withdrawal
was 41x365 = 14,965 billion gallons per year and the population
was 250 million. What was the per capita rate of water withdrawal?
Clearly state your units.
 Use the
functions W(t) and P(t) to create a new function C(t) to describe
the per capita water withdrawal. Clearly state your units.
 Graph
C(t). What trends do you see from the graph?
 Is the
per capita withdrawal rate increasing or decreasing?
 According
to the function C(t), what is the current per capita withdrawal
rate?
Reflection
Recently the
per capita use has been increasing. What would happen if the rate
remained constant from now on? In other words, what would happen
if the per capita rate stayed at the current level. Answer the questions
below using your work from above.
 Assume that
the per capita withdrawal rate doesn’t change from now on and
that the trend of the population function you derived continues.
 Write
a new function describing the total water withdrawal rate.
 What
is a reasonable domain for this function?
 Graph the
new function and the original function W(t) on the same coordinate
system.
 Compare
the two functions.
 How much
less water would be withdrawn in the next ten years?
 How is
this significant?

