Algebra
Chapter 3 Answers, Introducing Functions
Just as conserving energy can help preserve the environment, saving water can also help. Use the Internet to explore how much water you use for daily activities.
Part D, Making Connections
1. Look at the Water facts and trivia Web site. Use the information you find to help determine how much water the students at your school might use for showering.
a. Define two variable quantities for the relationship between the students at your school and the amount of water used.
[Let x = the number of students and y = the number of gallons of water used.]b. Assume every person in your school takes one 10-minute shower per day. Make a table of ordered pairs showing the relationship between the variables.
[Possible answers include: (1, 55); (2, 110); (3, 165); (4, 220); (5, 275); (6, 330); (7, 385); (8, 440); (9, 495); (10, 550)]c. Write an equation for the relationship between the variables. [y = 55x]
d. Graph the relationship.
e. Use your equation to find the amount of water needed by the students of your school for showers for one day.
[Possible answers include: If there are 2740 students, x = 2740. Since y = 55x, y = 55(2740). The number of gallons used by the students in this example is 150,700 gallons.]f. Using the Water facts and trivia site, predict how much rain must fall on an acre of land to provide enough water for the students at your school to shower for one day.
[Possible answers include: One inch of rainfall on an acre equals 27,000 gallons of water. If there are 2740 students, it would take 5.58 inches of rainfall on that acre to provide enough water for the students to shower one day.
How wasteful can a leak be? Let's investigate using water data from the Internet.
Part A, Understanding Linear Functions
1. Open the Water Leak Information Web site.
a. Make a chart for the first 10 days of the month indicating the total number of gallons of water that leaked.
Days 1
2
3
4
5
6
7
8
9
10
Gallons 15
30
45
60
75
90
105
120
135
150
b. Write an equation for the total number of gallons leaked.
[y = 15x, where x is the number of days the faucet has been dripping and y is the total number of gallons of water leaked.]c. Is y proportional to x? Explain.
[Yes, y is proportional to x, since y/x is the constant 15.]d. Predict whether or not the graph of your equation would be linear. Explain your reasoning.
[The graph is linear since the total number of gallons changes by an equal amount each day.]e. Graph your equation.
2. Look at the table, equation, and graph from 1. In which way do you think it is easiest to see the amount of water being wasted? Explain your answer. [Answers will vary.]