Ap calc bc frq 2022

Use the menu above to start your test prep with the best AP Calculus BC practice exams, free response questions, notes, videos, and study guides. A complete listing of the online resources that you need for your AP Calc review. AP Calculus BC Exam. This course is organized around the following big ideas: Big Idea 1: Limits; Big Idea 2: Derivatives

Ap calc bc frq 2022. AP® Calculus AB/BC 2022 Scoring Guidelines (b) Find the average value of the rate, in vehicles per hour, at which vehicles arrive at the toll plaza from 6 A.M. ( t = 1) to 10 A.M. ( t = 5 ). Average = ³5 A()t dt = 375.536966 −1 1 The average rate at which vehicles arrive at the toll plaza from 6 A.M. to 10 A.

CALCULUS BC FREE-RESPONSE QUESTIONS. The graphs of the polar curves r = 4 and r = 3 + 2 cos. p 5p. at q = and q = . 3 3. (a) Let R be the shaded region that is inside the graph of. q are shown in the figure above. The curves intersect. r = 4 and also outside the graph of r = 3 + 2 cos q , as shown in the figure above.

AP® Calculus AB/BC 2022 Scoring Guidelines Part B (AB or BC): Graphing calculator not allowed Question 4 9 points . General Scoring Notes The model solution is presented using standard mathematical notation. Answers (numeric or algebraic) need not be simplified. Answers given as a decimal approximation should bet 10, Bob’s velocity is modeled by B t. 3 2. 6 300, where t is measured in minutes and B t. is measured in meters per minute. Find Bob’s acceleration at time t 5. (d) Based on the model B from part (c), find Bob’s average velocity during the interval 0 t 10. dy. 4. Consider the differential equation.When businesses need to measure profit, they often consider the number of units sold for a set price. Incremental revenue is a way companies calculate the When businesses need to m...AP® CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES. feet per hour, t is measured in hours, and 0 ≤ t ≤ 8. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by D ( t ) = − 0.04 t 3 + 0.4 t 2 + 0.96 t cubic feet per hour, for 0 ≤ t ≤ 8. There are 30 cubic feet of water in the pipe ...Visit College Board on the web: collegeboard.org. AP® Calculus AB/BC 2022 Scoring Commentary. Question 1 (continued) In part (d) the response earned the first point with the equation on the left side of line 1. The middle expression, " A( t) − 400, " of the equation is not needed to earn that point. The second point was earned with the ...All of their 2022 video solutions can be viewed right here. 2022 AP Calculus BC Free Response Question 1 Solution [Student] You can check out this project from past years here (2021), here (2019), here (2018), here (2017), and here (2016). Many more Williston student screencasts can be found online right here. Posted in: AP Calculus BC.

Sample: 2C Score: 3. The response earned 3 points: 1 point in part (a), 1 point in part (b), no points in part (c), and 1 point in part (d). In part (a) the student earned the first point for the definite integral in the first line. The student did not earn the second point because the value produced is incorrect.® CALCULUS AB /CALCULUS BC AP The College Board. According to the model, 270 people 1 2018 SCORING GUIDELINES Question 1 (a) t ∫ 300 r( )dt =270 0 enter the line for the escalator45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes (graphing calculator required). Questions include algebraic, exponential, logarithmic, trigonometric, and general types of functions. Questions include analytical, graphical, tabular, and verbal ...This video presents a summary of scoring guidelines, solutions and common errors related to the 2022 AP Calculus FRQ AB1/BC1 question. The detailed solutions...This year, both AP Calculus exams are offered on May 13 th. The Nuts and Bolts of the AP Calculus Exams. Before you begin studying for an AP Calculus exam, let's look at the format of the tests. Both the AB and BC AP Calculus exams are structured the same way: A 30-question no-calculator multiple-choice section given over 60 minutes

In this video, we'll unpack a sample free-response question—FRQ (No Calculator).Download questions here: https://tinyurl.com/ye26cc54Stay motivated and keep ...Question 6 (continued) 1. in the second line by presenting the limit (with or without absolute values) lim 2 e n 3 . The response earned the. n 1 en second point by correctly evaluating the limit resulting in 1, referencing that 1 0 , and presenting a …t 10, Bob’s velocity is modeled by B t. 3 2. 6 300, where t is measured in minutes and B t. is measured in meters per minute. Find Bob’s acceleration at time t 5. (d) Based on the model B from part (c), find Bob’s average velocity during the interval 0 t 10. dy. 4. Consider the differential equation.Additional Resources for AP Calculus AB and BC Course Resources. Download. Commentary on FRQ Instructions Explains how answers are scored. PDF; 151.29 KB; Download. ... These AP Calculus Workshop materials from 2006-2007 focus on developing understanding, and teach this specific topic. PDF;2019 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B . Time—1 hour . Number of questions—4 . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The continuous function f is defined on the closed interval . −6 £ x £ 5. The figure above shows a portion of . the graph of . fDo we owe the emergence of language and self-reflection to the ancient and sustained consumption of psilocybin mushrooms? Advertisement Psychedelic research has experienced a renai...

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CollegeBoard has released a set of free response questions for Calculus BC: 2022 FRQ set. I thought that the non-calculator section was fairly difficult while the calculator section was pretty easy. FRQ’s from 1-4 weren’t bad either. Left like half of 5 blank though. Wasn't nearly as bad as my teacher made it out to be.AP Calculus. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday TicketWhen businesses need to measure profit, they often consider the number of units sold for a set price. Incremental revenue is a way companies calculate the When businesses need to m...The 2024 Calculus BC exam format will be: Section 1: Multiple Choice - 50% of your total score. 45 questions in 1 hr 45 mins. Part A: 30 questions in 60 minutes (calculator not permitted). Part B: 15 questions in 45 minutes (graphing calculator required). Section 2: Free Response - 50% of your total score. 6 questions in 1 hr 30 mins.The 2024 Calculus BC exam format will be: Section 1: Multiple Choice - 50% of your total score. 45 questions in 1 hr 45 mins. Part A: 30 questions in 60 minutes (calculator not permitted). Part B: 15 questions in 45 minutes (graphing calculator required). Section 2: Free Response - 50% of your total score. 6 questions in 1 hr 30 mins.

AP Calculus BC: Differential Equations on the Calculus BC Exam 2022 AP Live Bryan Passwater & Tony Record 4. Level: AP3 Which of the following differential equations models the slope field shown above? (A) dy yx dx (B) dy xy dx (C) dy xy dx (D) dy xy2 dx 5. Level: AP4 A hilarious meme about Bryan and Tony is spreading among AP Calculus students.2022 AP Calculus AB & AP Calculus BC Exam Free Response Question #1Full playlist: https://www.youtube.com/watch?v=9QeJBkrHlxA&list=PL6iwkLfBjZiz7vkRE1eBu9Axh...2019 AP ® CALCULUS AB FREE-RESPONSE QUESTIONS CALCULUS AB SECTION II, Part B . Time—1 hour . Number of questions—4 . NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS. 3. The continuous function f is defined on the closed interval . −6 £ x £ 5. The figure above shows a portion of . the graph of . fScoring notes: The first point is earned for a definite integral, with or without 1 1 1 or 3. 4 −. A response that presents a definite integral with incorrect limits but a correct integrand earns the first point. Presentation of the numerical value 9.875795 is not required to earn the second point.The AP Calculus BC exam has 2 sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes. Below is a summary of the different parts of ...Free Response Question 6 from the 2024 AP Calculus BC exam.The series question!Given a Maclaurin series we have to determine convergence of a series; use alt...Write your responses to this question only on the designated pages in the separate Free Response. booklet. Write your solution to each part in the space provided for that part. A particle, P, is moving along the x-axis. The velocity of particle P at time t is given by v t P () = sin t1.5. for 0 £ t £ p .1 ,, s!00 S 44ct(i-to) 'l= - :1 6: - o \t t U" t1,u_ !11)\t \OT - e Sea \oJor dlff{Y\j f1A1, -h "Mt t }e rvo. I O--t --)fJO JO + s r + D l -) d -Jo_ 0 .1 0 y 10 } )--q' J_( 0,H + 1'fu b 3o o: S,c61J e-&)i '· \ <t ()' 1 , fe of l.f: _ s, f l (,'nt fer eS /u<tor. C10 \' 1 1 . rl 1 1 . 1. People a line for an escalator at a rate modeled by the function r given byGet all the info on the AP Calculus BC Scoring & Score Distribution—including a score calculator to see where you stand. ... while Section II has seven free-response questions. Of the 7 questions in Section II, 4 are short-answer questions, and 3 are long-essay questions. ... let's examine how students fared in the 2022, 2021 and 2019 exams.

Write your responses to this question only on the designated pages in the separate Free Response booklet. Write your solution to each part in the space provided for that part. 2024 College Board. 4. The graph of the differentiable function f , shown for − x − , has a horizontal tangent at x £ 7 and is = 2 linear for x.

Ap Calculus Bc Frq 2024 Answers Ap. I loved how they let you leave a simple integral as an. Find the frqs from college board here: Bc test include an frq where you are given a table of data and asked to approximate a derivative with. 60 minutes (calculator not permitted). ... 2022 Ap Calculus Ab Frq 4 Youtube, 2024 ap calculus bc free response ...AP® Calculus BC 2002 Scoring Guidelines Form B. The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face ...AP AND DE EXPECTATIONS 2022-2023 ... AP Calculus AB AP Calculus BC Multivariable Calculus and Linear Algebra AP Statistics ... (free response questions), and separate calculator and non-calculator parts. The assessments are timed. End of the year: final Return to Top. exam at the end ofWalkthrough of the 2022 AP Calculus AB/BC FRQ #3 Join My Discord Study Server: https://discord.gg/8WGtt3r If you'd like extra resources for AP Calculus, ch...Visit College Board on the web: collegeboard.org. AP® Calculus AB/BC 2023 Scoring Commentary. Question 1 (continued) In part (d) the response earned the first point for the correct value of g′ ( 140 ) . The response earned the second point with the statement "at t = 140 seconds, the rate of flow of gasoline is changing at a rate of − .005.2022 AP Calculus BC Exam Free Response Question #5Full playlist: https://www.youtube.com/watch?v=9QeJBkrHlxA&list=PL6iwkLfBjZiz7vkRE1eBu9AxhU3fh8XEOarea & vo...12.2. 6.7. * The number of students with Calculus AB subscores may differ slightly from the number of students who took the AP Calculus BC Exam due to exam administration incidents. The following comments on the 2022 free-response questions for AP® Calculus AB and Calculus BC were written by the Chief Reader, Julie Clark of Hollins University.Bigfoot or an Ancient Ape? - Sasquatch researchers have no conclusive evidence that sasquatches exist. Learn about scientific explanations for the sasquatch, like the gigantopithec...AP Calculus BC Scoring Guide Unit 7 Progress Check: FRQ Part A Copyright © 2017. The College Board. These materials are part of a College Board program.CollegeBoard has released a set of free response questions for Calculus BC: 2022 FRQ set. I thought that the non-calculator section was fairly difficult while the calculator section was pretty easy. FRQ's from 1-4 weren't bad either. Left like half of 5 blank though. Wasn't nearly as bad as my teacher made it out to be.

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2022 AP Calculus BC Exam Free Response Question #6Full playlist: https://www.youtube.com/watch?v=9QeJBkrHlxA&list=PL6iwkLfBjZiz7vkRE1eBu9AxhU3fh8XEOseries pr...Question 6 (continued) 1. in the second line by presenting the limit (with or without absolute values) lim 2 e n 3 . The response earned the. n 1 en second point by correctly evaluating the limit resulting in 1, referencing that 1 0 , and presenting a correct. 2 2 conclusion in the lower right.We will review the free-response questions from the 2023 and 2022 AP calculus BC exams. Since the last question on the FRQ is most likely a series question, ...AP® Calculus AB/BC 2022 Scoring Guidelines . Part A (AB or BC): Graphing calculator required Question 1 9 points . General Scoring Notes . The model solution is presented using standard mathematical notation. Answers (numeric or algebraic) need not be simplified. Answers given as a decimal approximation should beMay 12, 2022 · Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship, beyond that, images of white ...A typical university-level calculus 1 and 2 course is more rigorous, covers about 33% more content (just a rough estimation from what I've seen so far), and requires out of the box thinking. It's a lot more enjoyable because it's not very straight forward and requires you to actually use your brain. With my knowledge from AP Calc BC, I ...Free-response questions with graphically presented functions have appeared regularly on AP ® exams (both AB and BC) over the last 20 years. Analyze functions using graphical information on Texas Instruments graphing calculators with examples from the 2022 AP ® Calculus AB and BC exams.The 2023 AP® Calculus BC exam has a passing rate of 78.5% and a mean score of 3.75, both of which are significantly higher than the passing rate and average score of AP® Calculus AB. ... The links below will take you to the AP® Calculus AB free-response questions for recent years: 2023 AP® Calculus AB Free-Response Questions; 2022 AP ... ….

Besides the complete practice test, the only official AP Calculus BC multiple choice practice questions are found in the AP Calculus Course and Exam Description. Beginning on page 228 there are 22 multiple-choice questions you can use to practice. The questions include answers and the major skills each question tests.AP Calculus. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday TicketAP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore …AP Calculus AB/BC Exams. Regularly Scheduled Exam Date: Monday morning, May 9, 2022 Late-Testing Exam Date: Friday morning, May 20, 2022. Section I. Total Time: 1 hour and 45 minutes Part A: Time: 1 hour. Number of Questions: 45 Number of No calculator allowed. Percent of Total Score: 50% Questions: 30.EVERYTHING YOU NEED TO HELP SCORE A PERFECT 5! Ace the AP Calculus BC Exam with this comprehensive study guide, which includes 4 full-length practice tests, content reviews, targeted strategies, and access to online extras. Techniques That Actually Work.- Tried-and-true strategies to help you avoid traps and beat the test- Tips for …Write your solution to each part in the space provided for that part. 6. Consider the curve given by the equation 6xy y. = 2 + . dy y. (a) Show that 2 . dx = y2 − 2x. (b) Find the coordinates of a point on the curve at which the line tangent to the curve is horizontal, or explain why no such point exists.2022 AP Calculus AB/BC FRQ 1 YouTube, 2 questions, 30 minutes, graphing calculator required. Ultimate guide to the ap calculus ab exam 2024. ... Source: www.youtube.com. AP Calculus AB & AP Calculus BC 2016 Exam FRQ 5 YouTube, Students are given 4 free response questions on a variety of skills throughout the course such as applying tests ...No matter what course you are taking, we are a community that helps students earn college credit! 2022 AP Calc BC Score Release Discussion! didn’t study at all (burnt out asf 😪) and somehow clutched a 5💀 on the series frq i literally wrote “please, i tried : (“ and called it a day 🤣. Ap calc bc frq 2022, Prepare for the AP Calculus BC free response questions with online resources. Review the prior year questions, watch the video solutions for 2022 and 2021, and try the sample questions from the College Board., Here's my own PDF solutions for the released 2023 AP exams for AP Calculus, Statistics, and Physics. If you're looking for help in AP Physics 1, check out a new course I've put together here AP Statistics PDF SolutionYouTube SolutionsFRQ #1 FRQ #2 FRQ #3FRQ #4FRQ #5 FRQ #6AP Calculus ABPDF Solution (AB)PDF Solution (BC) …, This is the regularly scheduled date for the AP Calculus BC Exam. Your school's AP coordinator can tell you where your exam will be administered. Resources. Article. AP Exams Overview . Get an overview of AP Exams, including exam timing and structure and the best ways to practice., The response earned the second point for the correct units presented in the boxed answer in line 2. Question 4 (continued) In part (b) the response earned the first point with the statements given in the last three lines, which place the value −6 between the values of −5.0 and −6.1., May 2, 2022. 1 min read. Predictions for the 2022 AP Calculus Exam. I am almost giddy each year when the free response questions are released. I love seeing what the College Board comes up with to test students' understanding of Calculus concepts. Before the exam, I like to spend time talking with my students about what I think is "due" to show ..., AP Calculus AB/BC Exams. Regularly Scheduled Exam Date: Monday morning, May 9, 2022 Late-Testing Exam Date: Friday morning, May 20, 2022. Section I. Total Time: 1 hour and 45 minutes Part A: Time: 1 hour. Number of Questions: 45 Number of No calculator allowed. Percent of Total Score: 50% Questions: 30., Sample: 1B. Score: 7. The response earned 7 points: 1 point in part (a), 2 points in part (b), 1 point in part (c), and 3 points in part (d). In part (a) the difference quotient of 10 - 6 in the first line would have earned the first point with no simplification. In., AP Calculus BC: Differential Equations on the Calculus BC Exam 2022 AP Live Bryan Passwater & Tony Record 4. Level: AP3 Which of the following differential equations models the slope field shown above? (A) dy yx dx (B) dy xy dx (C) dy xy dx (D) dy xy2 dx 5. Level: AP4 A hilarious meme about Bryan and Tony is spreading among AP Calculus students., May 11, 2022 ... Walkthrough of the 2022 AP Calculus AB FRQ #2 ✓ Join My Discord Study Server: https://discord.gg/8WGtt3r ✓ If you'd like extra resources ..., In this case, the response correctly simplifies to the boxed answer of ln 5 at the end of line 1 and earned the second point. The response confirms this answer with the sentence in line 2. In part (b) the response earned the first point with the correct definite integral ∫5 xe x 5 dx in line 2. The response. 1., AP Calculus BC Score Calculator for 2023, Frq #5 from the 2024 ap calculus ab exam.find the frqs from college board here: Ap calc ab frq 2024 calendar. Source: www.reddit.com. AP Calculus AB 2022 FRQ's All Answers. The scoring reports are not out, Ap calc bc (big children) discuss it right here!! Score higher on ap calculus 2024:, Every single AP Calculus AB and BC past paper including full papers, multiple choice, free response questions and practice papers from 1968 onwards. NEW Hiring - A Level Maths students (predicted an A*) or Further Maths students (predicted an A or A* ) to type solutions for worksheets & other resources (also looking for students with very neat ..., For more practice, visit the Albert guide to AP® Calculus AB-BC, where we've prepared hundreds of multiple-choice and free-response questions for you. Increase your chances for a passing score with Albert! For the 2015-2016 school year, students who utilized Albert resources for AP® Calculus AB overtook the national pass average by 12.34%!, Multiple-Choice and Free-Response Questions in Preparation for the AP Calculus BC Examination David Lederman 2011 Teaching AP Calculus Lin McMullin 2002. ... 5 Steps to a 5: AP Calculus BC 2022 William Ma 2021-08-04 MATCHES THE LATEST EXAM! Let us supplement your AP classroom experience with this easy-to-follow study guide. The immensely, We will review the free-response questions from the 2023 and 2022 AP calculus BC exams. Since the last question on the FRQ is most likely a series question, ..., Slope fields have been a topic on the AP Calculus BC Exam since 1998 and on the AP Calculus AB Exam since 2004. Teachers can find questions involving slope fields from the AP Exams on the following Released Exams: 1998 BC multiple-choice question 24 and free-response question 4. 2000 BC free-response question 6. 2002 BC free-response question 5., Every AB test and all but one (2019) BC test include an FRQ where you are given a table of data and asked to approximate a derivative with AROC or a definite integral with a Riemann sum. Often (like in 2021 #1 on both AB and BC) they ask you to do both., 2001 Scoring Commentary. The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement Program. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may ..., AP Calculus BC Score Calculator. To calculate your possible future AP Calculus BC score, use the sliders below to adjust the 1 multiple-choice section and 7 free response questions. The curve for this score calculator is based on the most recently available scoring guidelines. Section I: Multiple Choice. 30 /45., Visit College Board on the web: collegeboard.org. AP® Calculus AB/BC 2022 Scoring Commentary. Question 1 (continued) In part (d) the response earned the first point with the equation on the left side of line 1. The middle expression, “ A( t) − 400, ” of the equation is not needed to earn that point. The second point was earned with the ..., In this video, we'll unpack a sample free-response question—FRQ (No Calculator).Download questions here: https://tinyurl.com/2a6s32ctStay motivated and keep ..., 2022 RELEASED FREE RESPONSE SOLUTIONS – MR. CALCULUS 2022 BC #5 (no calculator) (a) (b) (c) Area R = 1 x ... 5/16/2022 5:39:40 PM ..., Be the first to review "AP Calculus BC-Real Past papers-Free Response Questions (FRQ) With Answers & Scoring Guidelines (2016-2023)" Cancel reply Your email address will not be published. Required fields are marked *, Knowing the task models for each question stem from College Board was a great help in our review sessions. As expected, each FRQ was planned to represent the task. FRQ #1: Function concepts FRQ #2: Modeling a non-periodic function in context FRQ #3: Modeling a periodic function in context FRQ #4: Symbolic function manipulations, Walkthrough of the 2022 AP Calculus AB/BC FRQ #3 Join My Discord Study Server: https://discord.gg/8WGtt3r If you'd like extra resources for AP Calculus, ch..., 2019 AP® CALCULUS BC FREE­RESPONSE QUESTIONS 5. Consider the family of functions 1 fx() x 2 − 2x k, where k is a constant. (a) Find the value of k, for k! 0, such that the slope of the line tangent to the graph of f at x 0 equals 6. (b) For k −8, find the value of fx d() 1 x 0 . (c) For k 1, find the value of fx d()x 0 2 or show that it diverges., CALCULUS BC SECTION II, Part A. Time—30 minutes Number of problems—2. A graphing calculator is required for these problems. 1. At time t, a particle moving in the xy-plane is at position ( x ( t ) , y ( t ) ) , where x ( t ) and y ( t ) are not explicitly ≥ dx = + dy given. For t 0, 4 t 1 and = sin ( t 2 ) ., CALCULUS BC SECTION II, Part A. A graphing calculator is required for these problems. 20 1. Water is pumped into a tank at a rate modeled by W t 2000 e liters per hour for 0 t 8, where t is measured in hours. Water is removed from the tank at a rate modeled by R t liters per hour, where R is differentiable and decreasing on 0 t 8., Commonly Seen Free Response Questions on the AP Calc Exam. While the AP Calc Exam presents students with with new, unique free response questions every year, looking at previous exams reveals some problem structures that are used repeatedly. For example, particle motion seem questions seem to show up almost every year, as do …, AP CALCULUS NEW FRQ Module 1: Approximating Values and Functions. An airplane takes off along a straight runway. For 0 ≤ t ≤ 2 0, the plane's velocity is given by a differentiable function v. Selected values of v t( ), where t is measured in seconds and v t( ) is measured in meters per second, are given in the table below., AP Classroom, AP Calculus BC Free Response 2012 Solutions iLearnMath.net. Problem 1. a) (15) (9) 67.9 61.8 6.1 degrees Fahrenheit '(12) 1.017 15 9 6 6 minute WW W | | . At. t 12minutes. , we estimate that the temperature of water is increasing at a rate approximately equal to the average rate of change between 9 and 15 minutes, which is 1.017 degrees ..., CALCULUS BC SECTION II, Part A. A graphing calculator is required for these problems. 20 1. Water is pumped into a tank at a rate modeled by W t 2000 e liters per hour for 0 t 8, where t is measured in hours. Water is removed from the tank at a rate modeled by R t liters per hour, where R is differentiable and decreasing on 0 t 8.