Review Topics

## Water Consumption in United States

### Comprehension

1. What is the main source of drinking water for your community?
2. What are other major uses for water in your community?
3. What factors could lead to an increase in the amount of water used each year?
4. What factors could lead to a decrease in the amount of water used each year?
5. Where does “used” water go?
6. 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 The table below lists only the amount of water (in billion gallons per day) withdrawn for public supply, such as drinking water.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) 180.7 194.3 205.1 216 227.7 238.5 250 263.1
Source: Statistical Abstract of the United States, U.S. Census Bureau

### To Determine:

1. Trends for water withdrawal;
2. Trends for U.S. population;
3. Trends for per capita withdrawal

### How much water do we use?

1. 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 To do this, assume that if W billion gallons are withdrawn in one year then the rate is W billion gallons per year.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).
1. Make points out of the data and plot them; use a (t,W) coordinate system.
2. 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.
3. 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?
2. Use the function W(t) to answer these questions.
1. Estimate the withdrawal rate in 1993.
2. Predict the withdrawal rate for 2004.
3. Predict when the annual withdrawal rate will reach 20,000 billion gallons per year.
3. 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).
4. Next, use the Riemann Sum Applet to find the total amount of water withdrawn from the year 2000 through 2020.
5. Estimate when the total withdrawal since the year 2000 reaches 800 billion gallons?

### How many people are using the water?

1. 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.
1. Make points out of the data and plot them; use a (t,P) coordinate system.
2. Use linear regression to fit the data with a linear function. Call this function P(t) and graph it.
3. What patterns do you see?
2. Use the function P(t) to answer these questions.
1. Estimate the population in 1993.
2. Predict the population for 2004.
3. Predict when the population will reach 300 million.

### How much water do we use per person?

1. Per capita water withdrawal rate means water withdrawal rate per person.
1. 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.
2. 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.
3. Graph C(t). What trends do you see from the graph?
4. Is the per capita withdrawal rate increasing or decreasing?
5. 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.

1. Assume that the per capita withdrawal rate doesn’t change from now on and that the trend of the population function you derived continues.
1. Write a new function describing the total water withdrawal rate.
2. What is a reasonable domain for this function?
2. Graph the new function and the original function W(t) on the same coordinate system.
1. Compare the two functions.
2. How much less water would be withdrawn in the next ten years?
3. How is this significant?