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: 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 US 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per day) withdrawn for public supply, such as drinking water.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
abstracts and you can research this if interested.)
Year 
1960 
1965 
1970 
1975 
1980 
1985 
1990 
1995 
Withdrawal
for public supply (billion gallons per day) 
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
Abstracts of the United States, US Census Bureau
Objectives
To Determine:
 Trend for
water withdrawal;
 Trend for
US population;
 Trend for
per capita withdrawal
Questions
How
much water do we use?
 We wish
to write a function that will describe 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that if W billion gallons are withdrawn in one year then the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 US 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 the 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 withdrawal rate will reach 20,000 billion gallons
per year.
 Use the
function W(t) and the integral to determine the amount of water
withdrawn in the US from 1990 through 2000.
 Next, use
the integral to find a function which gives the total amount
of water withdrawn from the year 2000 through an unspecified
year 2000 + x.
 When will
the total withdrawal since the year 2000 reach 290,000 billion
gallons?
How
many people are using the water?
 Next write
a function that describes US population. For this function,
Let P denote the US 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 capital 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 function.
 How
much less water would be withdrawn in the next ten years?
 How
is this significant?

