Hello,I would need to get this Calculus project done as follow:You will need to complete this this assignment as two different files.
You will need to complete and deliver back to me 2-pages for "Milestone One" attached:MAT 223 Milestone One Guidelines and Rubric.pdf >>>>> (as one separate file)
and 4-pages for the "Final Project" file attached:MAT 223 Final Project Guidelines and Rubric.pdf
(MAT 223 Final Project Scenarios.docx)>>>> Scenarios to get this done.
Please reach out to me or call me if you have any questions.Thanks!
MAT 223 Milestone One Guidelines and Rubric Overview: At its essence, calculus is the study of how things change. In the field of information technology, the practical applications of calculus span a wide variety of industries and other areas, from data analysis and predictive analytics to image, video, and audio processing; from physics engines for video games to modeling software for biological, meteorological, and climatological models; and from machine learning and artificial intelligence to measuring the rate of change in interest-accruing accounts or tumors. What all these applications have in common is understanding how objects change with respect to time. The derivative function represents a rate of change. We can take the derivative of a function by using either the limit definition of a derivative or the different differentiation rules. What do we do when we don’t have a given function, but only a set of data points? Scenario One: Motion Problem Prompt You have been hired by a firm that is designing a runway for an airport. Your job is to confirm that the runway is long enough for an airplane to land, but not unnecessarily long. You are given the velocity data for the largest aircraft that will land at the airport. The velocity data will be used to calculate the distance required for the aircraft to safely land and come to a stop. Below is a set of data that represents the velocity (in feet per second) of the final 45 seconds of the landing. At t = 0, the plane is on its final descent. Table I t in seconds 0 5 10 15 20 25 30 35 40 45 v(t) in feet per second 274.27 223.19 179.23 141.4 108.83 80.80 56.68 35.91 18.04 2.65 Table II t in seconds 4 5 14 15 24 25 34 35 44 45 v(t) in feet per second 232.8 223.19 148.52 141.4 86.08 80.80 39.82 35.91 5.55 2.65 Part II: Analysis of Data – Applying Derivatives A. Calculating average acceleration. Using the data in Table I, calculate the average acceleration for the following intervals: i. From t = 0 to t = 45 ii. From t = 25 to t = 45 iii. From t = 40 to t = 45 B. Calculating instantaneous acceleration. 1. Using the data in Table II, calculate the instantaneous acceleration at the following intervals: i. t = 5 ii. t = 15 iii. t = 25 iv. t = 35 v. t = 45 2. Explain how you used the limit definition of a derivative to calculate the instantaneous acceleration. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the acceleration at a maximum? How is this relevant to the landing aircraft? For each of the questions above, provide supporting solutions and calculus terminology to explain how you arrived at your answers. Also, explain in detail what your answer represents in a real-world context and why this is useful. Scenario Two: Decay Problem Prompt You have been hired by a company that has recently developed a medication designed to reduce the size of benign tumors. Your role is to confirm that the medication does reduce the size of the tumor, given the rate-of-change data. There are many factors to consider, and the goal is to determine the total change in the size of the tumor. Using this data, can you confirm that there is a change in the size of the tumor? Table I t in days 0 5 10 15 20 25 30 35 40 45 r(t) in mm per day 0 -0.0105 -0.02093 -0.03134 -0.04171 -0.05204 -0.06234 -0.07261 -0.08283 -0.09303 Table II t in days 4 5 14 15 24 25 34 35 44 45 r(t) in mm per day -0.00839 -0.0105 -0.02926 -0.03134 -0.04998 -0.05204 -0.07056 -0.07261 -0.09099 -0.09303 Part II: Analysis of Data – Applying Derivatives A. Calculating average change in the rate of change. Using the data in Table I, calculate the average change in the rate of change data for the following intervals: i. From t = 0 to t = 45 ii. From t = 25 to t = 45 iii. From t = 40 to t = 45 B. Calculating instantaneous change in the rate of change. 1. Using the data in Table II, calculate the instantaneous acceleration at the following intervals: i. t = 5 ii. t =15 iii. t = 25 iv. t = 35 v. t = 45 2. Explain how you used the limit definition of a derivative to calculate the instantaneous rate of change. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the rate of change at a maximum? How is this relevant to the size of the tumor? For each of the questions above, provide supporting solutions and calculus terminology to explain how you arrived at your answers. Also, explain in detail what your answer represents in a real-world context and why this is useful. Rubric Guidelines for Submission: Your final problem walkthroughs should be a 1- to 2-page Microsoft Word document with double spacing, 12-point Times New Roman font, and one-inch margins. Critical Elements Proficient (100%) Needs Improvement (75%) Not Evident (0%) Value Calculate the Average Rate of Acceleration/Change Correctly calculates the average rate acceleration/change over all given time intervals Applies correct calculus techniques to calculate average acceleration of each time interval, with minor errors in some calculations Does not accurately calculate the average rate of acceleration/change for a majority of time intervals 40 Instantaneous Acceleration / Rate of Change Correctly calculates the instantaneous acceleration / rate of change at all specific time values Applies correct calculus techniques in calculating instantaneous acceleration at all specific time values, with minor errors in calculation Does not accurately calculate the instantaneous acceleration / rate of change for a majority of time values 40 Application of Calculus Terminology in Explanation With Supporting Examples Correctly applies supporting solutions and calculus terminology to explain how answers were determined Applies correct calculus terminology in a majority of steps to explain how answers were determined, with some supporting solutions Does not apply calculus terminology in explanation, or does not support with examples to explain solutions 20 Total 100% 1 MAT 223 Final Project Guidelines and Rubric Overview At its essence, calculus is the study of how things change. In the field of information technology, the practical applications of calculus span a wide variety of industries and other areas, from data analysis and predictive analytics to image, video, and audio processing; from physics engines for video games to modeling software for biological, meteorological, and climatological models; and from machine learning and artificial intelligence to measuring the rate of change in interest-accruing accounts or tumors. What all these applications have in common is understanding how objects change with respect to time. The derivative function represents a rate of change. We can take the derivative of a function by using either the limit definition of a derivative or the different differentiation rules. What do we do when we don’t have a given function, but only a set of data points? There are two possible scenarios for the final project in this course. You must choose only one of the following options, which are outlined in the Final Project Scenarios document: 1. Motion Problem 2. Decay Problem You will create a report that illustrates your final answer, process, explanations, and detailed solutions. You will defend the validity of your solutions and demonstrate your ability to effectively communicate using calculus notations, conventions, and terminology. The project includes one milestone, which is an important opportunity to submit a draft of Part II and ensure the accuracy of your calculations. This milestone will be submitted in Module Five. The final product will be submitted in Module Seven. In this assignment, you will demonstrate your mastery of the following course outcomes: Interpret real-world problems by selecting mathematical theorems that appropriately address the problem Utilize appropriate calculus techniques for solving real-world problems Determine the behavior of functions by analyzing a real-world model through appropriate calculus techniques Defend mathematical processes and solutions using appropriate calculus terminology Prompt Specifically, the following critical elements must be addressed: I. Introduction: In this section, you will briefly describe the mathematical theorem you selected, what you are trying to answer with your report, the approach for how you arrived at this selection, and the data points related to the rate of change of the object and how you will use them to arrive at your final results. https://learn.snhu.edu/d2l/lor/viewer/view.d2l?ou=6606&loIdentId=20255 https://learn.snhu.edu/d2l/lor/viewer/view.d2l?ou=6606&loIdentId=20255 2 A. Briefly describe the mathematical theorems you selected and what you are trying to answer with your report. [MAT-223-01] B. Describe the approach for determining how you arrived at this selection. [MAT-223-01] C. Explain mathematically how the provided data will be used to arrive at your final results. [MAT-223-01] II. Analysis of Data: Applying Derivatives A. Using the given data, calculate the average acceleration of the changing object over given time intervals. [MAT-223-02] B. Using the given data, calculate the instantaneous acceleration at specific time values. [MAT-223-02] III. Analysis of Data: Applying Integrals A. Using the data provided, estimate the total change in the object. [MAT-223-02] 1. Use a right-endpoint estimate. 2. Use a left-endpoint estimate