Name: ___________________________________ # ___________ Honors Coordinate Algebra: Period _____________ Ms. Pierre Date: ______________ 3.6.1 Building Functions from Context Warm Up 1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that represents the cost of the mangoes. If each mango costs $1 this week, what is the total cost of his mangoes for this week? 2. Kerin drives at a speed of 55 miles per hour on the highway for her job. Write an equation that represents the distance she travels. If one day she drives for 6 hours, how many miles did she travel?
Transcript
Name: ___________________________________ # ___________ Honors Coordinate Algebra: Period _____________ Ms. Pierre Date: ______________
3.6.1 Building Functions from Context
Warm Up
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Lesson 3.6.1: Building Functions from ContextWarm-Up 3.6.1For each problem, write an equation to represent the situation and then answer the question.
1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that represents the cost of the mangoes. If each mango costs $1 this week, what is the total cost of his mangoes for this week?
2. Kerin drives at a speed of 55 miles per hour on the highway for her job. Write an equation that represents the distance she travels. If one day she drives for 6 hours, how many miles did she travel?
3. Mr. Stevens teaches 4 math classes. Depending on absences, the number of students in each class varies. Write an equation that represents the number of students Mr. Stevens teaches in a day. If there are 30 students in each class and one day all of the students were present, how many students did Mr. Stevens teach that day?
4. Jessica reads approximately 12 pages of her novel each hour. Depending on extracurricular activities and homework, the time that Jessica has to read varies. Write an equation that represents the number of pages Jessica reads. If Jessica read for 3 hours yesterday, approximately how many pages did she read?
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Lesson 3.6.1: Building Functions from ContextWarm-Up 3.6.1For each problem, write an equation to represent the situation and then answer the question.
1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that represents the cost of the mangoes. If each mango costs $1 this week, what is the total cost of his mangoes for this week?
2. Kerin drives at a speed of 55 miles per hour on the highway for her job. Write an equation that represents the distance she travels. If one day she drives for 6 hours, how many miles did she travel?
3. Mr. Stevens teaches 4 math classes. Depending on absences, the number of students in each class varies. Write an equation that represents the number of students Mr. Stevens teaches in a day. If there are 30 students in each class and one day all of the students were present, how many students did Mr. Stevens teach that day?
4. Jessica reads approximately 12 pages of her novel each hour. Depending on extracurricular activities and homework, the time that Jessica has to read varies. Write an equation that represents the number of pages Jessica reads. If Jessica read for 3 hours yesterday, approximately how many pages did she read?
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Lesson 3.6.1: Building Functions from ContextWarm-Up 3.6.1For each problem, write an equation to represent the situation and then answer the question.
1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that represents the cost of the mangoes. If each mango costs $1 this week, what is the total cost of his mangoes for this week?
2. Kerin drives at a speed of 55 miles per hour on the highway for her job. Write an equation that represents the distance she travels. If one day she drives for 6 hours, how many miles did she travel?
3. Mr. Stevens teaches 4 math classes. Depending on absences, the number of students in each class varies. Write an equation that represents the number of students Mr. Stevens teaches in a day. If there are 30 students in each class and one day all of the students were present, how many students did Mr. Stevens teach that day?
4. Jessica reads approximately 12 pages of her novel each hour. Depending on extracurricular activities and homework, the time that Jessica has to read varies. Write an equation that represents the number of pages Jessica reads. If Jessica read for 3 hours yesterday, approximately how many pages did she read?
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Lesson 3.6.1: Building Functions from ContextWarm-Up 3.6.1For each problem, write an equation to represent the situation and then answer the question.
1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that represents the cost of the mangoes. If each mango costs $1 this week, what is the total cost of his mangoes for this week?
2. Kerin drives at a speed of 55 miles per hour on the highway for her job. Write an equation that represents the distance she travels. If one day she drives for 6 hours, how many miles did she travel?
3. Mr. Stevens teaches 4 math classes. Depending on absences, the number of students in each class varies. Write an equation that represents the number of students Mr. Stevens teaches in a day. If there are 30 students in each class and one day all of the students were present, how many students did Mr. Stevens teach that day?
4. Jessica reads approximately 12 pages of her novel each hour. Depending on extracurricular activities and homework, the time that Jessica has to read varies. Write an equation that represents the number of pages Jessica reads. If Jessica read for 3 hours yesterday, approximately how many pages did she read?
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
This lesson requires the use of the following skills:
• evaluating expressions using multiplication, division, addition, and subtraction
• evaluating exponential expressions
IntroductionVerbal descriptions of mathematical patterns and situations can be represented using equations and expressions. A variable is a letter used to represent a value or unknown quantity that can change or vary in an expression or equation. An expression is a combination of variables, quantities, and mathematical operations; 4, 8x, and b + 102 are all expressions. An equation is an expression set equal to another expression; a = 4, 1 + 23 = x + 9, and (2 + 3)1 = 2c are all equations.
Drawing a model can help clarify a situation. When examining a pattern, look for changes in quantities. A function is a relation between two variables, where one is independent and the other is dependent. For each independent variable there is only one dependent variable. One way to generalize a functional relationship is to write an equation. A linear function can be represented using a linear equation. A linear equation relates two variables, and both variables are raised to the 1st power; the equation s = 2r – 7 is a linear equation. The slope-intercept form of a linear equation is y = mx + b. The form of a linear function is similar, f (x) = mx + b, where x is the independent quantity, m is the slope, b is the y-intercept, and f (x) is the function evaluated at x or the dependent quantity. The slope, or the measure of the rate of change of one variable with respect to another variable, between any two pairs of independent and dependent quantities is constant if the relationship between the quantities is linear. Consecutive terms in a pattern have a common difference if the pattern is linear.
An exponential function can be represented using an exponential equation. An exponential equation relates two variables, and a constant in the equation is raised to a variable; the equation w = 3v is an exponential equation. The general form of an exponential equation is y = ab x. The form of an exponential function is similar, f (x) = ab x, where a and b are real numbers. Terms have a common ratio if the pattern is exponential. An explicit equation describes the nth term of a pattern, and is the algebraic representation of a relationship between two quantities. An equation that represents a function, such as f (x) = 2x, is one type of explicit equation. Evaluating an equation for known term numbers is a good way to determine if an explicit equation correctly describes a pattern.
Key Concepts
• A situation that has a mathematical pattern can be represented using an equation.
• A variable is a letter used to represent an unknown quantity.
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
This lesson requires the use of the following skills:
• evaluating expressions using multiplication, division, addition, and subtraction
• evaluating exponential expressions
IntroductionVerbal descriptions of mathematical patterns and situations can be represented using equations and expressions. A variable is a letter used to represent a value or unknown quantity that can change or vary in an expression or equation. An expression is a combination of variables, quantities, and mathematical operations; 4, 8x, and b + 102 are all expressions. An equation is an expression set equal to another expression; a = 4, 1 + 23 = x + 9, and (2 + 3)1 = 2c are all equations.
Drawing a model can help clarify a situation. When examining a pattern, look for changes in quantities. A function is a relation between two variables, where one is independent and the other is dependent. For each independent variable there is only one dependent variable. One way to generalize a functional relationship is to write an equation. A linear function can be represented using a linear equation. A linear equation relates two variables, and both variables are raised to the 1st power; the equation s = 2r – 7 is a linear equation. The slope-intercept form of a linear equation is y = mx + b. The form of a linear function is similar, f (x) = mx + b, where x is the independent quantity, m is the slope, b is the y-intercept, and f (x) is the function evaluated at x or the dependent quantity. The slope, or the measure of the rate of change of one variable with respect to another variable, between any two pairs of independent and dependent quantities is constant if the relationship between the quantities is linear. Consecutive terms in a pattern have a common difference if the pattern is linear.
An exponential function can be represented using an exponential equation. An exponential equation relates two variables, and a constant in the equation is raised to a variable; the equation w = 3v is an exponential equation. The general form of an exponential equation is y = ab x. The form of an exponential function is similar, f (x) = ab x, where a and b are real numbers. Terms have a common ratio if the pattern is exponential. An explicit equation describes the nth term of a pattern, and is the algebraic representation of a relationship between two quantities. An equation that represents a function, such as f (x) = 2x, is one type of explicit equation. Evaluating an equation for known term numbers is a good way to determine if an explicit equation correctly describes a pattern.
Key Concepts
• A situation that has a mathematical pattern can be represented using an equation.
• A variable is a letter used to represent an unknown quantity.
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
• An expression is a combination of variables, quantities, and mathematical operations.
• An equation is an expression set equal to another expression.
• An explicit equation describes the nth term in a pattern.
• A linear equation relates two variables, and each variable is raised to the 1st power.
• The general equation to represent a linear function is f (x) = mx + b, where m is the slope and b is the y-intercept.
• An exponential equation relates two variables, and a constant in the equation is raised to a variable.
• The general equation to represent an exponential function is f (x) = ab x, where a and b are real numbers.
• Consecutive dependent terms in a linear function have a common difference.
• If consecutive terms in a linear pattern have an independent quantity that increases by 1, the common difference is the slope of the relationship between the two quantities.
• Use the slope of a linear relationship and a single pair of independent and dependent values to find the linear equation that represents the relationship. Use the general equation f (x) = mx + b, and replace m with the slope, f (x) with the dependent quantity, and x with the independent quantity. Solve for b.
• Consecutive dependent terms in an exponential function have a common ratio.
• Use the common ratio to find the exponential equation that describes the relationship between two quantities. In the general equation f (x) = ab x, b is the common ratio. Let a
0 be the
value of the dependent quantity when the independent quantity is 0. The general equation to represent the relationship would be: f (x) = a
0b x. Let a
1 be the value of the dependent quantity
when the independent quantity is 1. The general equation to represent the relationship would be: f (x) = a
1b x – 1.
• A model can be used to analyze a situation.
Common Errors/Misconceptions
• only examining the relationship between two terms to determine the general rule for a pattern
• confusing recursive and explicit equations
• incorrectly evaluating a recursive or explicit equation when determining if an equation matches a situation
Example 1
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
The starting balance of Anna’s account is $1,250. She takes $30 out of her account each month. How much money is in her account after 1, 2, and 3 months? Find an equation to represent the balance in her account at any month.
1. Use the description of the account balance to find the balance after each month.
Anna’s account has $1,250. After 1 month, she takes out $30, so her account balance decreases by $30: $1250 – $30 = $1220.
The new starting balance of Anna’s account is $1,220. After 2 months, she takes out another $30. Subtract this $30 from the new balance of her account: $1220 – $30 = $1190.
The new starting balance of Anna’s account is $1,190. After 3 months, she takes out another $30. Subtract this $30 from the new balance of her account: $1190 – $30 = $1160.
2. Determine the independent and dependent quantities.
The month number is the independent quantity, since the account balance depends on the month. The account balance is the dependent quantity.
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
• An expression is a combination of variables, quantities, and mathematical operations.
• An equation is an expression set equal to another expression.
• An explicit equation describes the nth term in a pattern.
• A linear equation relates two variables, and each variable is raised to the 1st power.
• The general equation to represent a linear function is f (x) = mx + b, where m is the slope and b is the y-intercept.
• An exponential equation relates two variables, and a constant in the equation is raised to a variable.
• The general equation to represent an exponential function is f (x) = ab x, where a and b are real numbers.
• Consecutive dependent terms in a linear function have a common difference.
• If consecutive terms in a linear pattern have an independent quantity that increases by 1, the common difference is the slope of the relationship between the two quantities.
• Use the slope of a linear relationship and a single pair of independent and dependent values to find the linear equation that represents the relationship. Use the general equation f (x) = mx + b, and replace m with the slope, f (x) with the dependent quantity, and x with the independent quantity. Solve for b.
• Consecutive dependent terms in an exponential function have a common ratio.
• Use the common ratio to find the exponential equation that describes the relationship between two quantities. In the general equation f (x) = ab x, b is the common ratio. Let a
0 be the
value of the dependent quantity when the independent quantity is 0. The general equation to represent the relationship would be: f (x) = a
0b x. Let a
1 be the value of the dependent quantity
when the independent quantity is 1. The general equation to represent the relationship would be: f (x) = a
1b x – 1.
• A model can be used to analyze a situation.
Common Errors/Misconceptions
• only examining the relationship between two terms to determine the general rule for a pattern
• confusing recursive and explicit equations
• incorrectly evaluating a recursive or explicit equation when determining if an equation matches a situation
Example 2
𝑓 𝑥 = 2 ∙ 2!!! = 2!
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
5. Evaluate the equation to verify that it is correct.
Organize your results in a table. Use the explicit equation to find each term. The terms that are calculated should match the terms in the original list.
The pairs of dependent and independent quantities match the ones in the original pattern, so the explicit equation is correct.
The balance in Anna’s account can be represented using the equation f (x) = –30x + 1250.
Example 2
Consider that the first figure below has two 180º angles, one on each side of the line segment. Each of these angles is then bisected or cut in half. This pattern continues, and the first 4 figures in the pattern are shown.
Write an equation to represent the relationship between the figure number and the number of angles in the figure.
1. Use the figures to determine the number of angles in figure numbers 1, 2, 3, and 4.
Count the angles in each figure, taking into consideration the note that the first figure has 2 angles.
Figure 1: 2 angles
Figure 2: 4 angles
Figure 3: 8 angles
Figure 4: 16 angles
Example 3
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
5. Evaluate the equation to verify that it is correct.
Organize your results in a table. Use the explicit equation to find each dependent term. The terms that are calculated should match the terms in the original list.
The dependent terms match the ones in the original pattern, so the explicit equation is correct.
The relationship between the number of angles and the figure number can be described using the equation f (x) = 2 • 2 x – 1.
Example 3
A video arcade charges an entrance fee, then charges a fee per game played. The entrance fee is $5, and each game costs an additional $1. Find the total cost for playing 0, 1, 2, or 3 games. Describe the total cost with an explicit equation.
1. Use the description of the costs to find the total costs.
If no games are played, then only the entrance fee is paid. The total cost for playing 0 games is $5.
If 1 game is played, then the entrance fee is paid, plus the cost of one game. If each game is $1, the cost of one game is $1. The total cost is $5 + $1 = $6.
If 2 games are played, then the entrance fee is paid, plus the cost of two games. If each game is $1, the cost of two games is $1 • 2 = $2. The total cost is $5 + $2 = $7.
If 3 games are played, then the entrance fee is paid, plus the cost of three games. If each game is $1, the cost of three games is $1 • 3 = $3. The total cost is: $5 + $3 = $8.
Guided Practice
1. )
2.)
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Practice 3.6.1: Building Functions from ContextWrite an explicit equation to represent each pattern below.
1. Mr. Ramos notices a pattern in the number of people attending the weekly student government meetings. For weeks 1, 2, 3, 4, and 5, the number of students attending the meeting was 31, 43, 55, 67, and 79, respectively.
2. Hannah borrows $30 from her parents. Each week, she pays them back the same amount. The total amounts she owes her parents after weeks 0, 1, 2, 3, and 4 are $30, $25, $20, $15, and $10, respectively.
3. Angelo sells cookies in packages, where each package contains the same number of cookies. The total amounts of cookies he has after 1, 2, 3, 4, and 5 packages are sold are 110, 88, 66, 44, and 22, respectively.
4. Cameron tracks the growth of leaves on a tree in his yard. Each week, he notes the number of open leaves on the tree. In weeks 1, 2, 3, 4, and 5, the tree has 12, 60, 300, 1,500, and 7,500 leaves, respectively.
5. As a treat, Nia eats a portion of a chocolate bar each day. She eats the same portion of the remaining bar each day. On day 0, the bar of chocolate starts with 32 pieces. After 1 day, 16 pieces remain. After days 2, 3, and 4, there are a total of 8, 4, and 2 pieces remaining.
6. Given the diagram below, describe the number of sides in Figure x.
Figure 1 Figure 2 Figure 3 Figure 4
continued
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Practice 3.6.1: Building Functions from ContextWrite an explicit equation to represent each pattern below.
1. Mr. Ramos notices a pattern in the number of people attending the weekly student government meetings. For weeks 1, 2, 3, 4, and 5, the number of students attending the meeting was 31, 43, 55, 67, and 79, respectively.
2. Hannah borrows $30 from her parents. Each week, she pays them back the same amount. The total amounts she owes her parents after weeks 0, 1, 2, 3, and 4 are $30, $25, $20, $15, and $10, respectively.
3. Angelo sells cookies in packages, where each package contains the same number of cookies. The total amounts of cookies he has after 1, 2, 3, 4, and 5 packages are sold are 110, 88, 66, 44, and 22, respectively.
4. Cameron tracks the growth of leaves on a tree in his yard. Each week, he notes the number of open leaves on the tree. In weeks 1, 2, 3, 4, and 5, the tree has 12, 60, 300, 1,500, and 7,500 leaves, respectively.
5. As a treat, Nia eats a portion of a chocolate bar each day. She eats the same portion of the remaining bar each day. On day 0, the bar of chocolate starts with 32 pieces. After 1 day, 16 pieces remain. After days 2, 3, and 4, there are a total of 8, 4, and 2 pieces remaining.
6. Given the diagram below, describe the number of sides in Figure x.
Figure 1 Figure 2 Figure 3 Figure 4
continued
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Practice 3.6.1: Building Functions from ContextWrite an explicit equation to represent each pattern below.
1. Mr. Ramos notices a pattern in the number of people attending the weekly student government meetings. For weeks 1, 2, 3, 4, and 5, the number of students attending the meeting was 31, 43, 55, 67, and 79, respectively.
2. Hannah borrows $30 from her parents. Each week, she pays them back the same amount. The total amounts she owes her parents after weeks 0, 1, 2, 3, and 4 are $30, $25, $20, $15, and $10, respectively.
3. Angelo sells cookies in packages, where each package contains the same number of cookies. The total amounts of cookies he has after 1, 2, 3, 4, and 5 packages are sold are 110, 88, 66, 44, and 22, respectively.
4. Cameron tracks the growth of leaves on a tree in his yard. Each week, he notes the number of open leaves on the tree. In weeks 1, 2, 3, 4, and 5, the tree has 12, 60, 300, 1,500, and 7,500 leaves, respectively.
5. As a treat, Nia eats a portion of a chocolate bar each day. She eats the same portion of the remaining bar each day. On day 0, the bar of chocolate starts with 32 pieces. After 1 day, 16 pieces remain. After days 2, 3, and 4, there are a total of 8, 4, and 2 pieces remaining.
6. Given the diagram below, describe the number of sides in Figure x.
Figure 1 Figure 2 Figure 3 Figure 4
continued
3.)
4.)
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
7. Given the diagram that follows, describe the number of blocks in Figure x.
Figure 1 Figure 2 Figure 3
8. A rural school uses a phone tree to reach parents when the school is closed. Each parent calls multiple parents to notify them of the school closing. These parents then each call multiple parents, and so on. The diagram below shows the number of parents called after each round of calls. Each dot represents a parent. Find an explicit equation to represent the number of parents called in any round x.
Round 1
Round 2
Round 3
9. A hotel charges a room fee per night, plus an additional fee if more than one guest is staying in a room. Good Nights hotel charges $150 per night for a room, plus $25 per guest if more than one guest is staying in a room. Find an explicit equation to represent the nightly cost for any number of guests.
10. The population of a city is growing. Each year, the population increases by approximately 10%, or 0.10 times the previous year’s population. The population this year is 10,000. Find an explicit equation to represent the population of the town in any year. Consider that year 0 is this year.
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Practice 3.6.1: Building Functions from ContextWrite an explicit equation to represent each pattern below.
1. Mr. Ramos notices a pattern in the number of people attending the weekly student government meetings. For weeks 1, 2, 3, 4, and 5, the number of students attending the meeting was 31, 43, 55, 67, and 79, respectively.
2. Hannah borrows $30 from her parents. Each week, she pays them back the same amount. The total amounts she owes her parents after weeks 0, 1, 2, 3, and 4 are $30, $25, $20, $15, and $10, respectively.
3. Angelo sells cookies in packages, where each package contains the same number of cookies. The total amounts of cookies he has after 1, 2, 3, 4, and 5 packages are sold are 110, 88, 66, 44, and 22, respectively.
4. Cameron tracks the growth of leaves on a tree in his yard. Each week, he notes the number of open leaves on the tree. In weeks 1, 2, 3, 4, and 5, the tree has 12, 60, 300, 1,500, and 7,500 leaves, respectively.
5. As a treat, Nia eats a portion of a chocolate bar each day. She eats the same portion of the remaining bar each day. On day 0, the bar of chocolate starts with 32 pieces. After 1 day, 16 pieces remain. After days 2, 3, and 4, there are a total of 8, 4, and 2 pieces remaining.
6. Given the diagram below, describe the number of sides in Figure x.
Figure 1 Figure 2 Figure 3 Figure 4
continued
Independent Practice
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Problem-Based Task 3.6.1: Texting for the WinLucas’s friend Isabel is performing in a singing competition. The winner of the competition will be determined by call-in votes. To help Isabel earn votes, Lucas sends text messages to 8 of his friends. He then asks each of his friends to send texts to 8 more friends, and asks his friends to ask each of their friends to send 8 texts. He is hoping this pattern will continue and that many people will receive text messages telling them to vote for Isabel. Call each set of text messages a “round” of text messages, where Lucas’s messages are the first round, Lucas’s friends messages are the second round, and so on. Assuming that no one sends texts to the same person, how many texts will be sent after x rounds of text messages?
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
Problem-Based Task 3.6.1: Texting for the WinCoaching Sample Responses
a. Draw a diagram to model the situation.
Start the diagram with Lucas, and the 8 friends whom he texts in Round 1. Then show each of the 8 people his friends text in Round 2.the 8 people his friends text in Round 2.
Problem-Based Task 3.6.1: Texting for the WinCoaching Sample Responses
a. Draw a diagram to model the situation.
Start the diagram with Lucas, and the 8 friends whom he texts in Round 1. Then show each of the 8 people his friends text in Round 2.the 8 people his friends text in Round 2.
Problem-Based Task 3.6.1: Texting for the WinCoaching Sample Responses
a. Draw a diagram to model the situation.
Start the diagram with Lucas, and the 8 friends whom he texts in Round 1. Then show each of the 8 people his friends text in Round 2.the 8 people his friends text in Round 2.
Practice 3.6.1: Building Functions from ContextWrite an explicit equation to represent each pattern below.
1. Mr. Ramos notices a pattern in the number of people attending the weekly student government meetings. For weeks 1, 2, 3, 4, and 5, the number of students attending the meeting was 31, 43, 55, 67, and 79, respectively.
2. Hannah borrows $30 from her parents. Each week, she pays them back the same amount. The total amounts she owes her parents after weeks 0, 1, 2, 3, and 4 are $30, $25, $20, $15, and $10, respectively.
3. Angelo sells cookies in packages, where each package contains the same number of cookies. The total amounts of cookies he has after 1, 2, 3, 4, and 5 packages are sold are 110, 88, 66, 44, and 22, respectively.
4. Cameron tracks the growth of leaves on a tree in his yard. Each week, he notes the number of open leaves on the tree. In weeks 1, 2, 3, 4, and 5, the tree has 12, 60, 300, 1,500, and 7,500 leaves, respectively.
5. As a treat, Nia eats a portion of a chocolate bar each day. She eats the same portion of the remaining bar each day. On day 0, the bar of chocolate starts with 32 pieces. After 1 day, 16 pieces remain. After days 2, 3, and 4, there are a total of 8, 4, and 2 pieces remaining.
6. Given the diagram below, describe the number of sides in Figure x.
Figure 1 Figure 2 Figure 3 Figure 4
continued
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
7. Given the diagram that follows, describe the number of blocks in Figure x.
Figure 1 Figure 2 Figure 3
8. A rural school uses a phone tree to reach parents when the school is closed. Each parent calls multiple parents to notify them of the school closing. These parents then each call multiple parents, and so on. The diagram below shows the number of parents called after each round of calls. Each dot represents a parent. Find an explicit equation to represent the number of parents called in any round x.
Round 1
Round 2
Round 3
9. A hotel charges a room fee per night, plus an additional fee if more than one guest is staying in a room. Good Nights hotel charges $150 per night for a room, plus $25 per guest if more than one guest is staying in a room. Find an explicit equation to represent the nightly cost for any number of guests.
10. The population of a city is growing. Each year, the population increases by approximately 10%, or 0.10 times the previous year’s population. The population this year is 10,000. Find an explicit equation to represent the population of the town in any year. Consider that year 0 is this year.
2.) 3.)
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
7. Given the diagram that follows, describe the number of blocks in Figure x.
Figure 1 Figure 2 Figure 3
8. A rural school uses a phone tree to reach parents when the school is closed. Each parent calls multiple parents to notify them of the school closing. These parents then each call multiple parents, and so on. The diagram below shows the number of parents called after each round of calls. Each dot represents a parent. Find an explicit equation to represent the number of parents called in any round x.
Round 1
Round 2
Round 3
9. A hotel charges a room fee per night, plus an additional fee if more than one guest is staying in a room. Good Nights hotel charges $150 per night for a room, plus $25 per guest if more than one guest is staying in a room. Find an explicit equation to represent the nightly cost for any number of guests.
10. The population of a city is growing. Each year, the population increases by approximately 10%, or 0.10 times the previous year’s population. The population this year is 10,000. Find an explicit equation to represent the population of the town in any year. Consider that year 0 is this year.
LINEAR AND EXPONENTIAL FUNCTIONSLesson 6: Building Functions
7. Given the diagram that follows, describe the number of blocks in Figure x.
Figure 1 Figure 2 Figure 3
8. A rural school uses a phone tree to reach parents when the school is closed. Each parent calls multiple parents to notify them of the school closing. These parents then each call multiple parents, and so on. The diagram below shows the number of parents called after each round of calls. Each dot represents a parent. Find an explicit equation to represent the number of parents called in any round x.
Round 1
Round 2
Round 3
9. A hotel charges a room fee per night, plus an additional fee if more than one guest is staying in a room. Good Nights hotel charges $150 per night for a room, plus $25 per guest if more than one guest is staying in a room. Find an explicit equation to represent the nightly cost for any number of guests.
10. The population of a city is growing. Each year, the population increases by approximately 10%, or 0.10 times the previous year’s population. The population this year is 10,000. Find an explicit equation to represent the population of the town in any year. Consider that year 0 is this year.
