BC FRQ Resources: AB Calculus Free Response Notebook 1999 - 2015 College Board (BC): Free Response Questions/Solutions 9. AP BC Quiz 3: FRQ Topics Review WS (Antiderivative Word Problem, Interpret Derivative Graphs) (Thurs 3/30) BC FRQ Quiz 3 10. BC Polar Curves/Polar Area Practice FRQs 11. Jan 29, 2022 · In this video, I go through the AP Calculus AB/BC Free Response question 3. This question covers ideas such as the Fundamental Theorem of Calculus, Definite ... AP® Calculus AB Scoring Statistics 2017 Free-Response Questions Question Mean . Standard Deviation Number of Possible Points ; 1 3.32 ; 2.34 : 9 : 2 4.01 ; 2.75 ; 9 : 3 3.63 ; 2.63 ; 9 : 4 1.54 ; ... www.collegeboard.org . CollegeBoard . Title: AP® Calculus AB Scoring Statistics 2017 Free-Response Questions Author: College Board Subject: AP ...AP CALC AB FRQ 2017 2017 ap calculus ab questions 2017 the college board. college board, advanced placement program, ap, ap central, and the acorn logo are Skip to document Ask an ExpertCALCULUS ® The College Board. 2A 2B 2C AP AB 2017 SCORING COMMENTARY Question 2 (continued) Sample: Score: 9 The response earned all 9 points: 2 points in part (a), 2 points in part (b), 2 points in part (c), and 3 points in part (d). In part (a) the student earned the first point for the definite integral ∫ 2 f (t) dt 0 and the second point for Problem 3 from the 2017 AP Calculus AB and BC Exams. The problem deals with a graph of a derivative and utilizing the graph to determine function and second ...2017 AP ® CALCULUS BC FREE-RESPONSE QUESTIONS CALCULUS BC SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function f is differentiable on the closed interval [−6, 5 ] and satisfies f (− ) 2 = 7. The graph of f ¢, the derivative of f, consists of a semicircle and three line segments, as shown in the figure …2019 . AP ® Calculus AB . Sample Student Responses and Scoring Commentary . Inside: Free Response Question 3 . R. Scoring Guideline . R. Student Samples . R. Scoring ...Walkthrough of the 2017 AP Calculus AB FRQ #1. Thanks for watching the video. I have a lot more free problem solving videos on my website for AP Calculus as ...2017 ap ® calculus ab free-response questions 2 d h 4. At time t 0 , a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius 0 t q C ( ) at time , and the internal temperature of the potato is greater than q 27 C ! 0 t for all times . 38) Mon (5/8) - AP CALCULUS AB EXAM DAY Monday May 8th @8am Main Gym I. Multiple-choice questions (MCs) Part A: Graphing calculator not permitted 30 MCs 60 minutes Part B: Graphing calculator required 15 MCs 45 minutes II. Free-response questions (FRQ) Part A: Graphing calculator required 2 FRQs 30 minutesIn this video I go over Problem 2 from the Free-Response Calculator-Allowed Section of the 2017 AP Calculus AB Practice Exam.Time— 1 hour Number of questions —4 2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTION S. 3. The function f is differentiable on the closed interval >-6, 5 @ and satisfies f 2 (-) 7.2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes Number of questions—2. A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by. the function A, where . Ah ()is measured in square ...2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function f is differentiable on the closed interval >−6, 5 @ and satisfies f (−2 ) 7. The graph of f , the derivative of f, consists of a semicircle and three line segments, as shown in the figure above.May 12, 2017 · Problem 5 from the 2017 AP Calculus AB Exam. The problem deals with position, velocity and acceleration functions for two particles moving along the x-axis. Walkthrough of the 2017 AP Calculus AB FRQ #4. Thanks for watching the video. I have a lot more free problem solving videos on my website for AP Calculus as ...2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes Number of questions—2. A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by. the function A, where . Ah …AP Calculus BC Scoring Guidelines 2017 Author: The College Board Subject: AP Calculus BC Scoring Guidelines 2017 Keywords: AP Calculus BC Scoring Guidelines 2017; exam information; exam resources; scoring information Created Date: 7/11/2017 7:19:06 AMMore. We're excited to once again share with you our early solutions to this year's AP Calc AB Free Response Questions. We love seeing the new questions and working through them, always amazed at the original ways the College Board incorporates multiple concepts into a single question. Some of of our exam predictions turned out to be spot on ... 2022 AP Exam Free Response Solutions. AP Calculus 2017 AB FRQ Solutions Louis A. AP Calculus AB Practice Exams Free Response Notes Videos Study Guides Here ...2019 . AP ® Calculus AB . Sample Student Responses and Scoring Commentary . Inside: Free Response Question 3 . R. Scoring Guideline . R. Student Samples . R. Scoring ...Problem 1 from the 2017 AP Calculus AB and BC Exams. The problem deals with using cross sectional areas to model the volume of a tank. Part c involves the Fu...2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB . SECTION II, Part B . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function . f . is differentiable on the closed interval [−6, 5 ] and satisfies . f (− ) 2 = 7. The graph of . f ¢, the . derivative of . f, consists of a semicircle and three line segments, as shown in the ...The response earned 9 points: 1 point in part (a), 1 point in part (b), 4 points in part (c), and 3 points in part (d). In part (a) the response earned the point because the solution curve passes through 0,0 , is increasing and concave2017 AP Calculus BC — AB Subscore Scoring Worksheet Section I: Multiple Choice ... Section II: Free Response . Question 2. × 1.0000 = (out of 9) (Do not round ...Within each individual free-response question, at most one point is not earned for inappropriate rounding. Scoring guidelines and notes contain examples of the most common approaches seen in student responses. ... AP® Calculus AB/BC 2021 Scoring GuidelinesAP® Calculus AB/BC Exam. Regularly Scheduled Exam Date: Thursday morning, May 5, 2016 Late-Testing Exam Date: Thursday morning, May 19, 2016. Section I Total Time, Calculus AB: 1 hr. 45 min. Section II Total Time, Calculus AB: 1 hr. 30 min. Section I Total Time, Calculus BC: 1 hr. 45 min. Section II Total Time, Calculus BC: 1 hr. 30 min.AP Calculus AB 2015 Free-Response Questions Author: ETS Subject: Free-Response Questions from the 2015 AP Calculus AB Exam. Keywords: exam; 2015; Free-Response Questions; Calculus AB Created Date: 2/16/2015 7:51:58 AM 2017 AP® Calculus AB Free-Response Questions; 2016 AP® Calculus AB Free-Response Questions; 2015 AP® Calculus AB Free-Response Questions; You can also find examples of the multiple choice exam questions for the AP® Calculus AB exam here. There are only a few multiple-choice questions in the guide, so it can’t cover …May 12, 2017 · Problem 6 from the 2017 AP Calculus AB Exam. The problem deals with derivatives (product rule, chain rule) and utilizing tables and graphs to determine deriv... Model Solution Scoring Use the data in the table to estimate f ′(2.25). Using correct units, interpret the meaning of your answer in the context of this problem. Scoring notes: To earn the first point the response must provide both a difference and a quotient and must explicitly use values of f from the table.2017: Free-Response Questions; Questions. Scoring. Samples and Commentary. Free-Response Questions. Scoring Guidelines. Chief Reader Report. Scoring Statistics. Scoring Distributions. Sample Responses Q1. Sample Responses Q2. Sample Responses Q3. Sample Responses Q4. Sample Responses Q5. Sample Responses Q6Sample Student Responses and Scoring Commentary Inside: •Free Response Question 6 •Scoring Guideline •Student Samples •Scoring Commentary AP®CALCULUS AB 2017 SCORING GUIDELINES © 2017 The College Board. Visit the College Board on the Web: www.collegeboard.org. Question 6 (a) f x x xe′( ) ( )−+ =2sin 2 cossinx2017 AP Calculus AB Exam Free Response Question #5Particle motion problem. Given position of particle P and velocity of particle Q. Determine direction of ...AP® Calculus AB Scoring Statistics 2017 Free-Response Questions 2017 The College Board. Visit the College Board on the Web: www.collegeboard.orgCalculus: Learn Calculus with examples, lessons, worked solutions and videos, Differential Calculus, Integral Calculus, Sequences and Series, Parametric Curves and Polar Coordinates, Multivariable Calculus, and Differential, AP Calculus AB and BC Past Papers and Solutions, Multiple choice, Free response, Calculus Calculator.AP CALC AB FRQ 2017 2017 ap calculus ab questions 2017 the college board. college board, advanced placement program, ap, ap central, and the acorn logo are Skip to document Ask an ExpertProblem 1 from the 2017 AP Calculus AB and BC Exams. The problem deals with using cross sectional areas to model the volume of a tank. Part c involves the Fu... The following comments on the 2017 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response question and of how students performed on the question, including typical student errors. GeneralThe Calculus BC AP exam is a superset of the AB exam. It covers everything in AB as well as some of the more advanced topics in integration, sequences and function approximation. ... 2017 AP Calculus AB/BC 4b (Opens a modal) 2017 AP Calculus AB/BC 4c (Opens a modal) AP Calculus BC 2015. Learn. ... 2011 Calculus BC free response #1a (Opens a ...AP Calculus AB Practice Exams Free Response Notes Videos Study Guides. Here are the resources you will need for the AP Calculus AB free response questions. Be sure to try out the prior year questions and check out the video solutions. Working through these problems is an important part of your FRQ test prep.AP® Calculus AB 2013 Free-Response Questions . About the College Board . The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is2015 Frq Ap Calc AbHere is what I have for FRQ#1 and 2. AP Calculus AB 2015 Free Response Question 2 Let f and g be the functions defined by f (x) = 1+ x + ...AP Calculus AB 2017 Free Response Question 1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A, …12 мая 2017 г. ... 2017 AP Calculus AB & AP Calculus BC Exam Free Response Question #3 Note: In part d, I got the slope of a line wrong! (Nice work me!)2022 AP Exam Free Response Solutions. AP Calculus 2017 AB FRQ Solutions Louis A. AP Calculus AB Practice Exams Free Response Notes Videos Study Guides Here ...AP Calculus AB 2023 Free-Response Questions Author: ETS Subject: Free-Response Questions from the 2023 AP Calculus AB Exam Keywords: Calculus AB; Free-Response Questions; 2023; exam resources; exam information; teaching resources; exam practice Created Date: 4/14/2023 10:29:22 AM2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS. 4. At time t 0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal. temperature of …2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 2. When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by where ft()is measured in pounds per hour and t is the number of hours after the store opened. After the The following comments on the 2017 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-response question and of how students performed on the question, including typical student errors. General 17 мар. 2023 г. ... ... Calculus AB exam each year than take the AP® Calculus BC exam. This ... 2017 AP® Calculus AB Free-Response Questions · 2016 AP® Calculus AB ...In this video I go over the first problems 25 through 28 of the Multiple-Choice Section of the 2017 AP Calculus AB Practice Exam.Calculus BC Calculus AB Subscore Number of Students Scored 139,195 Score Distribution Exam Score N %At Global Mean 4.04 The following comments on the 2019 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Stephen Davis of Davidson College. They give an overview of each free-responseSample Student Responses and Scoring Commentary Inside: •Free Response Question 6 •Scoring Guideline •Student Samples •Scoring Commentary AP®CALCULUS AB 2017 SCORING GUIDELINES © 2017 The College Board. Visit the College Board on the Web: www.collegeboard.org. Question 6 (a) f x x xe′( ) ( )−+ =2sin 2 cossinxCalculus: Learn Calculus with examples, lessons, worked solutions and videos, Differential Calculus, Integral Calculus, Sequences and Series, Parametric Curves and Polar Coordinates, Multivariable Calculus, and Differential, AP Calculus AB and BC Past Papers and Solutions, Multiple choice, Free response, Calculus Calculator.Problem 1 from the 2017 AP Calculus AB and BC Exams. The problem deals with using cross sectional areas to model the volume of a tank. Part c involves the Fu... 2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes Number of questions—2. A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by. the function A, where . Ah …2016 AP Calculus AB Exam Free Response Question #4Differential equation with slope field. Draw a slope field. Write a tangent line and use it for an approx...AP Calculus AB Scoring Guidelines Author: College Board Subject: 2018 AP Exam Administration Keywords: AP Scoring Guidelines; 2018 AP Exam Administration; Advanced Placement; scoring information; scoring resources; exam resources; exam information; teacher resources; student resources; ADA Created Date: 6/22/2018 4:54:13 PMYou may not discuss or share the free-response exam content with anyone unless it is released on the College Board website in about two days. Your AP Exam score ...AP ® CALCULUS AB/CALCULUS BC 2019 SCORING COMMENTARY . Question 4 (continued) include a factor of . dh dt. Thus the second point was not earned, and the response is not eligible for the third point. In part (c) the response earned the first point with a correct separation of variables 1 1. dh dt h. 10 in line 2 on the left. The correct ... AP® CALCULUS AB 2019 SCORING COMMENTARY Question 2 (continued) quotient . 55 55 . 2.5 Numerical simplification is not required. The response simplifies the difference quotient to 0 in line 3 of the boxed work, and the first point was earned. In lines 1, 2, and 3 of the boxed work, the response earned the second point with “[s]ince . v. P (tIn this video I go over Problem 6 from the Free-Response Non-Calculator Section of the 2017 AP Calculus AB Practice Exam.Problem 4 from the 2017 AP Calculus AB and BC Exam Free Response section.Within each individual free-response question, at most one point is not earned for inappropriate rounding. Scoring guidelines and notes contain examples of the most common approaches seen in student responses. AP Calculus AB 2017 free response: AP Calculus AB solved free response questions from past exams AP Calculus AB 2015 free response: AP Calculus AB solved free ...Unit 12: AP Calculus AB solved free response questions from past exams. About this unit. ... (as always, best to pause the videos and try them yourself before Sal does). AP Calculus AB 2017 free response. Learn. 2017 AP Calculus AB/BC 4a (Opens a modal) 2017 AP Calculus AB/BC 4b (Opens a modal) 2017 AP Calculus AB/BC 4c (Opens a modal)From the 2017 Administration Calculus AB Practice Exam This exam may not be posted on school or personal websites, nor ... Free -Response Questions . Multiple-Choice Answer Key . Free-Response Scoring Guidelines ... Look at your exam packet and confirm that the exam title is “AP Calculus AB” or “AP Calculus BC,” depending upon …12 мая 2017 г. ... 2017 AP Calculus AB & AP Calculus BC Exam Free Response Question #3 Note: In part d, I got the slope of a line wrong! (Nice work me!)BC FRQ Resources: AB Calculus Free Response Notebook 1999 - 2015 College Board (BC): Free Response Questions/Solutions 9. AP BC Quiz 3: FRQ Topics Review WS (Antiderivative Word Problem, Interpret Derivative Graphs) (Thurs 3/30) BC FRQ Quiz 3 10. BC Polar Curves/Polar Area Practice FRQs 11. AP CALCULUS AB/CALCULUS BC 2017 SCORING COMMENTARY Question 1 (continued) Sample: 1B Score: 6 The response earned 6 points: the units point, 2 points in part (a), 1 point in part (b), 1 point in part (c), and 1 point in part (d). The units point was earned because the units of ft 3 in parts (a) and (c) and ft 3 /minute in part (d) 2015 Frq Ap Calc AbHere is what I have for FRQ#1 and 2. AP Calculus AB 2015 Free Response Question 2 Let f and g be the functions defined by f (x) = 1+ x + ...2022 AP Calculus AB Exam Free Response Question #2Full playlist: https://www.youtube.com/watch?v=9QeJBkrHlxA&list=PL6iwkLfBjZiz7vkRE1eBu9AxhU3fh8XEOarea …AP® CALCULUS AB/CALCULUS BC 2017 SCORING GUIDELINES Question 3 (a) ∫ −6 −2 f (−6)= f (−2)+ f ′(x) dx = 7 − f ′(x) dx =74 − =3 −2 ∫ −6 5 f ( 5 ) = f (−2 ) + ∫ f ′(x) dx = 7 −2 π +=3 10 π 2− −2 3 1 : uses initial condition : 1 : f (−6) 1 : f (5 ) (b) )f′(x) > and 0 on the intervals [−−2 6, (2, 5 ).2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS dH2 dt 2 4. At time t 0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius ()qC at time t 0, and the internal temperature of the potato is greater than 27 Cq for all times t ! 0. 2017 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB . SECTION II, Part B . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function . f . is differentiable on the closed interval [−6, 5 ] and satisfies . f (− ) 2 = 7. The graph of . f ¢, the . derivative of . f, consists of a semicircle and three line segments, as shown in the ...In this video I go over Problem 6 from the Free-Response Non-Calculator Section of the 2017 AP Calculus AB Practice Exam.
Walkthrough of the 2017 AP Calculus AB FRQ #6. Thanks for watching the video. I have a lot more free problem solving videos on my website for AP Calculus as .... Dollar general money order
AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes . Number of questions—2 . A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. People enter a line for an escalator at a rate modeled by the function r given by ⎧ ⎪ t t. 3 7 ⎪⎪ 44 1 for 0 ££ t ⎪ ()(rt ()=⎨ 100 300− ) 300 ...2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The function f is differentiable on the closed interval >−6, 5 @ and satisfies f (−2 ) 7. The graph of f , the derivative of f, consists of a semicircle and three line segments, as shown in the figure above. AP Calculus AB Practice Exams Free Response Notes Videos Study Guides. Here are the resources you will need for the AP Calculus AB free response questions. Be sure to try out the prior year questions and check out the video solutions. Working through these problems is an important part of your FRQ test prep. 2014 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT PAGE.38) Mon (5/8) - AP CALCULUS AB EXAM DAY Monday May 8th @8am Main Gym I. Multiple-choice questions (MCs) Part A: Graphing calculator not permitted 30 MCs 60 minutes Part B: Graphing calculator required 15 MCs 45 minutes II. Free-response questions (FRQ) Part A: Graphing calculator required 2 FRQs 30 minutes2017 AP Calculus AB & AP Calculus BC Exam Free Response Question #4Separable differential equation. Finding equation of a tangent line. Using a tangent lin...Both the AP Calculus AB and BC tests include a section of six free response (FR) questions. These questions differ in many ways from standard multiple choice problems. In this post, we’ll talk about a few tips to help you conquer the AP Calculus free response questions. Tip #1: Don’t Panic (and Be Prepared)15 .) Using correct units, interpret the meaning of the value in the context of the problem. (c) Find the timeAP Calculus AB Scoring Guidelines Author: College Board Subject: 2018 AP Exam Administration Keywords: AP Scoring Guidelines; 2018 AP Exam Administration; Advanced Placement; scoring information; scoring resources; exam resources; exam information; teacher resources; student resources; ADA Created Date: 6/22/2018 4:54:13 PM... exam may no longer perfectly align with the ap exam. Ap calculus ab 2017 practice exam. Download free-response questions from past exams along with scoring ...38) Mon (5/8) - AP CALCULUS AB EXAM DAY Monday May 8th @8am Main Gym I. Multiple-choice questions (MCs) Part A: Graphing calculator not permitted 30 MCs 60 minutes Part B: Graphing calculator required 15 MCs 45 minutes II. Free-response questions (FRQ) Part A: Graphing calculator required 2 FRQs 30 minutes: answer : { 1 : value 1 : meaning : 1 : considers f (5) and 1 : answer with reason g(5) 2 : integrals 3 : { : answer AP® CALCULUS AB 2017 SCORING COMMENTARY Question 2 Overview The context for this problem is the removal and restocking of bananas on a display table in a grocery store during{ : approximation : overestimate with reason : { 1 : integral : answer dt 3 : 2 : dV 1 : answer 2 2 (a) ∫ f ( t ) dt = 0AP CALC AB FRQ 2017 2017 ap calculus ab questions 2017 the college board. college board, advanced placement program, ap, ap central, and the acorn logo are Skip to …May 9, 2017 · Contents . Exam Instructions . Student Answer Sheet for the Multiple-Choice Section . Section I: Multiple-Choice Questions . Section II: Free -Response Questions 2017 AP® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part A Time—30 minutes Number of questions—2 A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. 1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A, where A(h) …AP® Calculus AB 2012 Free-Response Questions . About the College Board . The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is2017 AB AP Calculus Free-Response Solutions and Notes Question AB-1 (a) The left Riemann sum approximation is 50.3 2 14.4 3 6.55 cubic feet. 1 (b) This is an overestimate of the volume of the tank since A()h is decreasing. (c) The volume is 10 0 f hdh 101.325 cubic feet. 2 AP® Calculus AB 2010 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations.Model Solution Scoring Use the data in the table to estimate f ′(2.25). Using correct units, interpret the meaning of your answer in the context of this problem. Scoring notes: To earn the first point the response must provide both a difference and a quotient and must explicitly use values of f from the table.Problem 2 from the 2017 AP Calculus AB Exam. The problem deals with competing rates of change (the rates at which bananas are removed from and then placed on....
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