Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 2: Recursion...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 2: Recursion and Linear Functions 1. Coen decides to take a job with a company that sells magazine subscriptions. He is paid $20 to start selling and then earns $1.50 for each subscription he sells. Fill in the following table, showing the amount of money (M) Coen earns for selling n subscriptions. Use the process column to note what is happening in each line. n 0 Process Mn Mo= M = M = M3 = M4= 2. Write a recursive rule for the amount of money Coen can earn selling magazine subscriptions. 3. REFLECTION: The rule in Question 2 defines a term (Mn + 1) with respect to the term that precedes it (Mn). Write a rule that defines a term (Mn) with respect to the term that precedes it (Mn - 1)? How is this rule similar to and different from the rule you wrote in Question 2? 4. Write an explicit function rule for the nth term in the sequence describing the amount of money Coen can earn. Describe any domain restrictions in your rule. How is this rule related to the rules you wrote in Question 2? Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 2: Recursion and Linear Functions 5. Use sequence notation to enter the data from your table in Question 1 in a graphing calculator, if your calculator has this capability. Limit your lists to 50 entries each. How do you expect the scatterplot of your data to look? Justify your reasoning. 6. How much does Coen earn if he sells 100 magazine subscriptions? Which rule did you use to answer this question? Why did you choose that rule? 7. Coen is trying to earn enough money to buy a new MP3 player. He needs $225 to cover the cost and tax on the MP3 player. How many magazine subscriptions does Coen need to sell to buy his new MP3 player? Justify your answer. Which rule did you use to answer this question? Why did you choose that rule? 8. Your phone service allows you to add international long distance to your phone. The cost is a $5 flat fee each month and 3 a minute for calls made. Write a recursive rule describing your monthly cost for international calls. Then write a function rule for the n minutes of calls made in a month. 9. REFLECTION How are recursive rules different from explicit function rules for modeling linear data? How are they the same? When are recursive rules more useful than function rules? When are function rules more useful? 10. EXTENSION: Think of a situation that can be described by a linear function. Model the situation using a recursive rule and a function rule. Write a question that is better answered using the recursive rule and give the solution. Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions Different balls bounce at various heights depending on things like the type of ball, the pressure of air in the ball, and the surface on which it is bounced. The rebound percentage of a ball is found by determining the quotient of the rebound height (that is the height of each bounce) to the height of the ball before that bounce, converted to a percentage. 1. Collect data on a bouncing ball that show the maximum height of at least five bounces of the ball. Then make a scatterplot of the maximum height as a function of the bounce number. (Let Bounce 0 be the initial drop height of the ball.) Bounce No. Height 0 1 2 3 4 5 Height 41 2 5 Bounce 2. Find the average rebound percentage for your ball. Show your work. Bounce No. Height 0 1 2 3 4 5 Process Rebound Percentage Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions 3. Tennis balls are sealed in a pressurized container to maintain the rebound percentage of the balls. A tennis ball has a rebound percentage of 55% when it is taken out of the pressurized can. Suppose a tennis ball is dropped from a height of 2 meters onto a tennis court. Use the rebound rate given to predict the height of the ball's first seven bounces. Bounce No. 0 1 2 3 4 5 6 7 Process (initial drop height given) Height (m) 2 4. Write a recursive rule for the height of the ball for each successive bounce. 5. Describe, in words, how the height of each bounce is calculated from the height of the previous bounce. Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions 6. Enter the bounce height data into a graphing calculator. Make a scatterplot and then sketch the graph below. Height 6 4 21 5 Bounce # 7. What kind of function might model the tennis ball bounce situation? Explain your reasoning with a table of values or other representation. 8. Look back at the table you generated in Question 3. Write a function rule for bounce height in terms of bounce number. Graph the function rule with the scatterplot on your graphing calculator to see if the function rule models the data. 9. What is the height of the fifth bounce of a new tennis ball if the initial drop height is 10 meters above the ground? Use a function rule to find your answer. 10. Suppose a new tennis ball is dropped from a height of 20 feet. How many times does it bounce before it has a bounce height of less than 4 inches (the diameter of the ball)? Explain your solution. 11. What is the total vertical distance that the ball from Question 10 has traveled after six bounces? Explain your answer. 12. REFLECTION: How can you decide if a data set can be modeled by an exponential function? How are recursive rules different from function rules for modeling exponential data? How are they the same? Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 2: Recursion and Linear Functions 1. Coen decides to take a job with a company that sells magazine subscriptions. He is paid $20 to start selling and then earns $1.50 for each subscription he sells. Fill in the following table, showing the amount of money (M) Coen earns for selling n subscriptions. Use the process column to note what is happening in each line. n 0 Process Mn Mo= M = M = M3 = M4= 2. Write a recursive rule for the amount of money Coen can earn selling magazine subscriptions. 3. REFLECTION: The rule in Question 2 defines a term (Mn + 1) with respect to the term that precedes it (Mn). Write a rule that defines a term (Mn) with respect to the term that precedes it (Mn - 1)? How is this rule similar to and different from the rule you wrote in Question 2? 4. Write an explicit function rule for the nth term in the sequence describing the amount of money Coen can earn. Describe any domain restrictions in your rule. How is this rule related to the rules you wrote in Question 2? Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 2: Recursion and Linear Functions 5. Use sequence notation to enter the data from your table in Question 1 in a graphing calculator, if your calculator has this capability. Limit your lists to 50 entries each. How do you expect the scatterplot of your data to look? Justify your reasoning. 6. How much does Coen earn if he sells 100 magazine subscriptions? Which rule did you use to answer this question? Why did you choose that rule? 7. Coen is trying to earn enough money to buy a new MP3 player. He needs $225 to cover the cost and tax on the MP3 player. How many magazine subscriptions does Coen need to sell to buy his new MP3 player? Justify your answer. Which rule did you use to answer this question? Why did you choose that rule? 8. Your phone service allows you to add international long distance to your phone. The cost is a $5 flat fee each month and 3 a minute for calls made. Write a recursive rule describing your monthly cost for international calls. Then write a function rule for the n minutes of calls made in a month. 9. REFLECTION How are recursive rules different from explicit function rules for modeling linear data? How are they the same? When are recursive rules more useful than function rules? When are function rules more useful? 10. EXTENSION: Think of a situation that can be described by a linear function. Model the situation using a recursive rule and a function rule. Write a question that is better answered using the recursive rule and give the solution. Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions Different balls bounce at various heights depending on things like the type of ball, the pressure of air in the ball, and the surface on which it is bounced. The rebound percentage of a ball is found by determining the quotient of the rebound height (that is the height of each bounce) to the height of the ball before that bounce, converted to a percentage. 1. Collect data on a bouncing ball that show the maximum height of at least five bounces of the ball. Then make a scatterplot of the maximum height as a function of the bounce number. (Let Bounce 0 be the initial drop height of the ball.) Bounce No. Height 0 1 2 3 4 5 Height 41 2 5 Bounce 2. Find the average rebound percentage for your ball. Show your work. Bounce No. Height 0 1 2 3 4 5 Process Rebound Percentage Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions 3. Tennis balls are sealed in a pressurized container to maintain the rebound percentage of the balls. A tennis ball has a rebound percentage of 55% when it is taken out of the pressurized can. Suppose a tennis ball is dropped from a height of 2 meters onto a tennis court. Use the rebound rate given to predict the height of the ball's first seven bounces. Bounce No. 0 1 2 3 4 5 6 7 Process (initial drop height given) Height (m) 2 4. Write a recursive rule for the height of the ball for each successive bounce. 5. Describe, in words, how the height of each bounce is calculated from the height of the previous bounce. Using Recursion in Models and Decision Making: Recursion in Exponential Growth and Decay IV.B Student Activity Sheet 3: Recursion and Exponential Functions 6. Enter the bounce height data into a graphing calculator. Make a scatterplot and then sketch the graph below. Height 6 4 21 5 Bounce # 7. What kind of function might model the tennis ball bounce situation? Explain your reasoning with a table of values or other representation. 8. Look back at the table you generated in Question 3. Write a function rule for bounce height in terms of bounce number. Graph the function rule with the scatterplot on your graphing calculator to see if the function rule models the data. 9. What is the height of the fifth bounce of a new tennis ball if the initial drop height is 10 meters above the ground? Use a function rule to find your answer. 10. Suppose a new tennis ball is dropped from a height of 20 feet. How many times does it bounce before it has a bounce height of less than 4 inches (the diameter of the ball)? Explain your solution. 11. What is the total vertical distance that the ball from Question 10 has traveled after six bounces? Explain your answer. 12. REFLECTION: How can you decide if a data set can be modeled by an exponential function? How are recursive rules different from function rules for modeling exponential data? How are they the same?
Expert Answer:
Related Book For
Business Law and the Legal Environment
ISBN: 978-1111530600
6th Edition
Authors: Jeffrey F. Beatty, Susan S. Samuelson, Dean A. Bredeson
Posted Date:
Students also viewed these mathematics questions
-
The table below shows the potential output combinations of oranges and jars of prickly pear jelly (from the flower of the prickly pear cactus) for Florida and Arizona. a. Compute the opportunity cost...
-
Discuss Planning & Preparation in relation to: Preparing work documents and performing document review Preparing an audit plan
-
In problems 25-30, find the limits if And (See Example 4). 1. 2. 3. lim f(x) = 3 lim g(x) = -1 lim VF(x)g(x) 2f(x) 3g(x) f(x)+g(x) inm xa lim Vst) fx) +3)
-
The main propulsion system of a space shuttle consists of three identical rocket engines which provide a total thrust of 6 MN. Determine the rate at that the hydrogen-oxygen propellant is burned by...
-
Find an article about writing summary judgment motions from the courts perspective. What tips are given for writing a summary judgment motion?
-
On January 1, 2012, Quinton Corporation issued $600,000 of 7% bonds that are due in 10 years. The bonds were issued for $559,229 and pay interest each July 1 and January 1. The company uses the...
-
If sales for the 1st year are $10000, 2nd year are $15000 and 3rd year are $7000. The depreciation is $5000 each year. Fixed cost are $2000 every year and variable cost 10% of sales. If the tax rate...
-
In an attempt to locate fuser potential coverage needs, a producer interviews a prospective client who owns a home covered by an HO-3 policy. For which of the following items does the client already...
-
A 34-year-old man comes to the Emergency Department for review. He is HIV positive and continues to have unprotected sexual intercourse with males, despite having been warned not to, usually in...
-
What asset is used by watsonx.governance to organize all the models attempting to solve a single business problem?
-
what is the Audit Control Objective related to audit tools?
-
Cash =$10,000,Contributed Capital =$35,000 Beginning Retained Earnings =$11,000, Dividends =$8,000 Revenues =$55,000, Accounts Payable =$15,000 Equipment =$40,000, Expenses =$33,000 What is the net...
-
For the function f(x)=x' **1 calculate the compositions (fof)(x) and (fofof)(x). State the domain of each function. (fof)(x)= (fofof)(x)= Work: Domain: Domain:
-
For this assignment, you will apply what you have learned in this unit to a small business. To get the businesss finances under control, you need to prepare a budget. You may consider items from your...
-
(a) Water flows through the nozzle of a garden hose. Find an expression for m in terms of line pressure P 1 , ambient pressure P 2 , inside hose diameter D 1 , and nozzle outlet diameter D 2 . Assume...
-
In 1966, Arketex Ceramic Corp. sold land in rural Indiana to Malcolm Aukerman. The deed described the southern boundary as the section line between sections 11 and 14 of the land. Farther south than...
-
John C. Clark, using an alias, rented a Lexus from Alamo Rent-A-Car in San Diego, California. Clark never returned the car to Alamo and obtained a California quick title using forged signatures. He...
-
American Bakeries had a fleet of over 3,000 delivery trucks. Because of the increasing cost of gasoline, the company was interested in converting the trucks to propane fuel. It signed a requirements...
-
A system of three parallel reactions (Trambouze and Piret, 1959) involves the following reaction scheme: \[\mathrm{A} \xrightarrow{k_{1}} \mathrm{~B} \quad \mathrm{~A} \xrightarrow{k_{2}} \mathrm{C}...
-
Consider a binary equimolar mixture of acetone and chloroform at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). Because this mixture forms a binary azeotrope, methyl- \(n\)-pentyl ether solvent is used...
-
Repeat Exercise 8.1, taking the first two reactions as first order, and the last as second order with \(k_{1}=0.02 \mathrm{~min}^{-1}, k_{2}=0.2 \mathrm{~min}^{-1}\), and \(k_{3}=2.0 \mathrm{~L} /...
Study smarter with the SolutionInn App