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Lesson 2.1 Assignment
Name
Date
The Plane! Modeling Linear Situations
2
The E & W Light Company charges their customers $0.14 per kilowatt-hour used. The E & W Company sends the customers their bills monthly. 1. Use the scenario to complete the following questions. a. Identify the independent and dependent quantities and their units for this problem situation. Explain your reasoning.
b. Write the independent and dependent quantities and their units in the table. Then calculate the total cost for each of the given kilowatt-hours used. In the last row of the table, write an expression to represent the dependent quantity. Independent Quantity
c. Calculate the unit rate of change between three different pairs of points. What do you notice about the rates?
2
2. Consider the function in the form c(x) to describe the cost after using x kilowatt-hours of electricity. a. Write the function. What function family does this represent?
What Goes Up Must Come Down Analyzing Linear Functions
2
1. Lin and her friend Thomas are collecting food for the local food bank. Their goal is to collect a total of 1785 pounds of food. They start with 225 pounds donated by a local grocery store. Their goal is to collect 20 pounds of food per day. a. Identify the independent and dependent quantities and their units in this situation. Then complete the table. Independent Quantity
Chang-Ho is going on a trip to visit some friends from summer camp. He will use $40 for food and entertainment. He will also need money to cover the cost of gas. The price of gas at the time of his trip is $3.25 per gallon. 1. Consider a function in the form C(g) to represent this problem situation. a. Write a function to represent the total cost of the trip as a function of the number of gallons used.
b. Identify the independent and dependent quantities and their units.
c. Identify the rate of change and the y-intercept. Explain their meanings in terms of the problem situation.
d. Graph the function representing this situation on the coordinate plane. y Total Cost of Trip (dollars)
e. Use the graph to determine how many gallons of gas Chang-Ho can buy if he has $170 saved for the trip. Draw an oval on the graph to represent the solution. Then write your answer in words and as an inequality.
2 f. Verify the solution set you interpreted from the graph.
g. Chang-Ho’s mom gives him some money for his trip. He now has a total of $220 saved for the trip. What is the greatest number of gallons of gas he can buy before he runs out of money? Show your work and graph your solution on the number line.
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Chapter 2 Assignments
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Lesson 2.3 Assignment
Name
page 3
Date
h. If Chang-Ho spent more than $92 on his trip, how much gas could he have bought? Show your work and graph your solution on the number line.
2
Chang-Ho is on his way to visit his friends at camp. Halfway to his destination, he realizes there is a slow leak in one of the tires. He checks the pressure and it is at 26 psi. It appears to be losing 0.1 psi per minute. 2. Write a function, p(t), to show the tire’s pressure as a function of time in minutes.
3. Chang-Ho knows that if the pressure in the tire goes below 22 psi it may cause a tire blowout. What is the greatest amount of time that he can drive before the tire pressure hits 22 psi? Show your work and graph the solution.
We’re Shipping Out! Solving and Graphing Compound Inequalities
2
1. Taneisha’s family has signed up for a new cell phone plan. Taneisha now has a limit on the number of texts she can send or receive each month. She can text no more than 300 times per month. a. What is the least number of texts she can make in a month?
b. Write an inequality to represent the statement. Use n for the number of texts.
c. What is the greatest number of texts she can make in a month?
d. Write an inequality to represent the statement. Use n for the number of texts.
e. Write the statements from parts (b) and (d) as a compound inequality.
g. Graph the inequality. Describe your number line representation.
Chapter 2 Assignments
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Lesson 2.4 Assignment
page 2
2. Taneisha’s family’s new cell phone plan costs $55 per month plus $0.20 for each text with a maximum of 300 texts per month. Let t represent the number of texts made during the month. a. Write an expression to represent the total monthly cost of the plan.
2
b. Determine the minimum cost per month by using the least number of texts Taneisha can make in a month.
c. Write an inequality to represent the statement. Use c for the monthly cost.
d. Determine the maximum cost per month by using the greatest number of texts Taneisha can make in a month.
e. Write an inequality to represent the statement. Use c for the monthly cost.
g. Write the compound inequality in compact form.
h. Graph the inequality. Describe your number line representation.
f. Write the compound inequality that represents the cost of the plan.
Chapter 2 Assignments
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Lesson 2.4 Assignment
Name
page 3
Date
3. John owns a 50-acre apple orchard. Among his many concerns during the growing season is the amount of rainfall. Unfavorable conditions such as drought and flooding will affect tree production. John does not want rainfall amounts to be less than 10 inches or more than 50 inches.
2
a. Represent the undesirable rainfall amounts on the number line.
b. Write a compound inequality to represent the same information. Define your variable.
4. At John’s apple orchard, the profit he will make depends on the number of bushels he grows and sells. He makes $25 per bushel but must subtract $300,000 for costs associated with growing the trees in order to calculate his profit. a. Write an expression to represent the profit John will make. Let b represent the number of bushels he will produce and sell.
b. John must make at least $80,000 to pay the bills, but he does not want to make more than $250,000 because it will put him in a higher tax bracket. Write a compound inequality that represents the amount of profit John can make.
Play Ball! Absolute Value Equations and Inequalities
2
1. The Billingsly Cookie Company is experimenting with a new low-fat cookie recipe. The management wants the bakers to come up with a cookie that is low in fat but still has good taste. The company decides on a target fat content of 5 grams per cookie. In order to be labeled low-fat, a difference of 1.8 grams per cookie is acceptable. This means the amount of fat should be no more than 1.8 grams above 5 or no more than 1.8 grams below 5. a. Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content. Use f to represent the amount of fat in a cookie from the new recipe.
b. Write an absolute value inequality to represent the restrictions on the difference in the amount of fat.
c. One of the bakers creates a cookie recipe that has 6.5 grams of fat per cookie. Is this recipe acceptable? Explain your reasoning.
d. Another baker comes up with a cookie recipe that has 2.9 grams of fat per cookie. Is this recipe acceptable? Explain your reasoning.
Chapter 2 Assignments
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Lesson 2.5 Assignment
page 2
e. Algebraically determine the greatest and least number of grams of fat a cookie can contain and still fall within the required specifications. Write your answer as an inequality.
2
2. Shaderra is on a diet, so she is keeping track of the number of calories she eats each day. She is trying to eat 2000 calories a day but allows for a difference of 40 calories. She has already consumed all but 140 of her allotted calories today and is in the mood for a snack. She knows that each of the new low-fat cookies she loves has 20 calories. a. Write an expression that represents the difference between the amount of calories that will result from eating x number of cookies and the remaining calories Shaderra can consume today.
b. Write a linear absolute value equation that represents the allowable amount of calories she can consume today.
c. Determine the minimum and maximum number of cookies she can eat and still stay within an acceptable difference from her daily calorie count.
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Lesson 2.6 Assignment
Name
Date
Choose Wisely! Understanding Non-Linear Graphs and Inequalities
2
1. A scientist is researching certain bacteria that have been found recently in the large animal cages at a local zoo. He starts with 200 bacteria that he intends to grow and study. He determines that every hour the number of bacteria increases by 25%.
This problem situation is represented by one of the following functions:
f(t) 5 t2 1 1.25t 1 200
f(t) 5 |1.25t 1 200|
f(t) 5 200(1.25)t
f(t) 5 1.25t 1 200
a. Which function represents this problem situation? Explain your reasoning.
b. Complete the table to represent the amount of bacteria as a function of the number of hours it is in the growth medium. Independent Quantity
c. Use the data collected in the table to create a graph of the situation, then estimate the number of hours the scientist should let the bacteria grow to have no more than 2000 bacteria. y 3600
d. Determine the exact number of hours the bacteria can grow but not exceed 2000. Explain your method. Write your answer as an inequality.
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Lesson 2.6 Assignment
page 3
Name
Date
2. The cost per family to join the Grove Heights swimming pool is $375. In order to get the pool ready for the summer, renovation and painting are needed each spring. The pool asks the members to help complete the work. For every hour a family member works during the spring, the pool will reduce the membership fee by $10.
2
This problem situation is represented by one of the following functions:
f(t) 5 375 2 10t
f(t) 5 |210t 1 375|
f(t) 5 210t2 1 10t 1 37
f(t) 5 375(10)t
a. Which function represents this problem situation? Explain your reasoning.
b. Complete the table to represent the total membership fee as a function of the number of hours worked. Independent Quantity
