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This project is due in three parts. First part is selecting a topic and professor will give feedback on it. due 5/16/2020.After I receive the feedback for part 1, you will start working on part 2. Second part is Model the topic using a differential equation. a)Draw any visuals (diagrams), b)Write the differential equation, c) Classify the differential equation and its due on 6/4/2020.The 3rd and final part is the whole project(part 1-5). Again I will receive feedback from professor for part 2 and then you will start working on finishing the full project. And final project is due on 6/18/2020.Project: Submit a report in which you describe and analyze a real-world scenario for which ordinary differential equations apply. Research applications for ordinary differential equations and submit the following reports at each milestone. Your final submission should include the following critical elements.The details for the project is attached in pdf file. You must use equation tool in MS word for any equation you add in the project.all works must be cited accordingly. application_assignment_guidelines_and_grading_guide.pdf Unformatted Attachment Preview MAT 330: Application Assignment Guidelines and Grading Guide Overview The purpose of this assignment is to guide you through the process of developing a differential equation model, solving the resulting initial value problem, and interpreting the solution in the context of a real-world application. Completing the assignment will enable you to make a connection between what you are learning about differential equations and the world in which we live. Economists, engineers, linguists, biologists, and many other professionals use models based on differential equations, and this activity will give you a glimpse of how differential equations apply to everyday life. The assignment submission process is organized into two milestones and a final submission. At each milestone, you will submit a portion of the overall assignment to scaffold learning and to ensure quality final submissions. These milestone submissions will be made at the conclusion of Module Two and Module Five. The final submission will be due in Module Seven. Assignment Requirements Submit a report in which you describe and analyze a real-world scenario for which ordinary differential equations apply. Research applications for ordinary differential equations and submit the following reports at each milestone. Your final submission should include the following critical elements: 1. Select a topic that can be modeled by a first-order ordinary differential equation. Note that your topic should generate a differential equation that can be solved by the techniques in this course. Chapter 3 of our text introduces the modeling process and examples of applications that can be found throughout the text. Additionally, it is not hard to find interesting applications by searching the internet. Example topics:       Crime scene investigation using Newtons law of cooling Population growth models, with either unconstrained or constrained growth Simple dynamic models of mathematical economics, such as the change in the price of a product related to stock levels of that product Interest rate models involving loans or investments, such as determining the largest loan affordable that can be paid off in a given time period when considering a fixed-rate mortgage with monthly payments Modeling the velocity of a sprinter Carbon dating  Drug concentration in the human body 2. Model the topic using a differential equation. a) Draw any visuals (diagrams) that exemplify the model and facilitate understanding of the modeling process. Your visuals should represent the topic and help develop the differential equation. b) Write the differential equation that models your topic of choice. Define all the variables used in the model, and be sure to include initial conditions. c) Classify the differential equation, including the order and if it is linear or nonlinear. 3. Solve the differential equation using the techniques from this course. a) Provide a valid solution to the differential equation. Be sure to apply the initial conditions that youdeveloped. b) Discuss the method used to solve the differential equation. Explain all steps in arriving at the solution, writing in paragraph form and in complete sentences. 4. Discuss the solution in context of the initial topic. Write the solution of the differential equation in terms of the initial topic you chose in Part 1. Describe how this could be useful for someone in the field from which the model was obtained. Include solution values or graphics to illustrate the utility and applicability of the solution in the context of the topic youchose. 5. Discuss what you learned from the modeling process. Write one to two paragraphs pertaining to what you can take away from the modeling process in general. Deliverable Milestones Milestone 1 2 Module Due Determine the topic of your choice. Submit Two the topic only to your instructor (Part 1). Your instructor must approve before you can move forward. Develop the model and solve the Five differential equation. You should include only the differential equation, variables and initial conditions, and solution (Part 2b and Part 3a only). Deliverables You can choose to include the classification of the differential equation, any visuals, and method used to solve, but that is not required in this milestone. Parts 1–5: Final Submission Seven Grading Ungraded but required. Your topic must be approved by the instructor before you can move forward. Graded at 50 points for submission. Graded separately at 200 points; Final Product Rubric Final Product Rubric Requirements of submission: Written components of project must follow these formatting guidelines when applicable: double spacing, 12point Times New Roman font, 1-inch margins, and discipline-appropriate citations. An equation tool must be used for all mathematical formulas and equations. Critical Elements Topic Selection Exemplary (100\%) Submission meets “Proficient” criteria and effectively describes the interest in the topic of choice Submission meets “Proficient” criteria and describes each component of the visual and its connection to the topic of choice Submission meets Differential “Proficient” criteria and Equation includes explicit variable definitions and initial conditions Classification of Submission meets Differential Equation “Proficient” criteria and describes why it is classified as such Solution to Submission meets Differential Equation “Proficient” criteria and solution is written using clear displayed math Model Visuals Proficient (85\%) Submission contains a real- world topic that can be modeled by a first-order differential equation Submission contains a visual representation of the model in order to facilitate the modeling process Differential equation accurately describes the model Submission includes the classification of the differential equation Solution is correct and initial conditions are applied Needs Improvement (55\%) Submission contains a topic that can be modeled by differential equation, but does not have a realworld application or it cannot be modeled by a differential equation in the scope of this course Submission contains some visual representation of the model, but it does not fully represent the reality of the topic Differential equation does not accurately describe the model Not Evident (0\%) Submission does not include a real-world topic modeled by a first-order differentialequation Submission includes partial or incorrect classification of differential equation Solution is incorrect or submission does not include the correct application of the initial conditions Value 5 Submission does not contain any visual representation to describe the model 15 Submission does not contain a differential equation to solve 20 Do attempt to classify the differential equation 10 No attempt to solve the differential equation 15 Method to Solve Submission meets “Proficient” criteria and further extends the explanation to why that method was chosen Solution in Context to Initial Topic Lessons Learned Submission meets “Proficient” criteria and further illustrates the applicability in the context of the topic Submission describes in words the method used to solve the differential equation Submission includes the solution in terms of the topic and includes how it could be useful in the field Submission includes a summary of what was learned from the differential equation modeling process Submission describes the method from the course used to solve the differential equation, but the description is incomplete or not in paragraph form Submission does not include how the model and solution are used in the field Submission does not include the method used to solve the differential equation 10 No solution in terms of the topic of choice is provided 15 Summary of the modeling process is lacking in personal tone or is not appropriate to the topic Submission does not include lessons learned from the modeling process 10 Total 100\% ... 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