differential equation

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Mathematics

Kennesaw State University

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SAVING FOR A CHILD’S COLLEGE EDUCATION You will work in groups of two on this assignment. A first draft is due Monday, September 9. The final draft is due Monday, September 30. You will submit this assignment on D2L. STATEMENT Model what you will do to completely pay for a child’s college education. It is most important that you (1) (2) (3) (4) make clear assumptions, build a mathematical model, perform a complete analysis, summarize your actions, and perform a sensitivity analysis, i.e. address the question, “What would slight changes in your assumptions or parameters do to your plan?” Consider a full four year (or more) college education at KSU. 1 2 RUBRIC Each of the following elements are rated along a range of 0 − 4, depending on the completeness and quality of the work on that element. (1) Organization: You must have the following organizational elements in the final paper, each with a clear header. • Problem Introduction Section • Model Section • Mathematical Analysis Section • Prediction and Evaluation Section • Credits: Give credit to people that assisted you or references you used (if any) (2) Layout and Formatting: This is a report, not an assignment, so please write this paper in narrative (paragraph) format, except putting equations and formulas on separate lines. Here are further guidelines: • Narratives in paragraphs. Typed 11 or 12 point font. • Equations and calculations, etc. are on a separate line and easy to read. • Understandability of graphs. (Suggestion: You may take a picture of hand drawn graphs and of graphs on calculators or other software.) • Clear identification of graphs in the narratives through labeling of the graphs (e.g., “see Figure 1”). • Graphs are used effectively in the narratives and explanations. In other words, you refer to the graphs and use the graphs in your discussions. (3) Introduction: Must include: • Introduction of the problem. (Summarize the problem in your own words.) • Discuss how this problem may be similar and different from other applied problems you have encountered. (4) Model: Must include: • Clear mathematical statement of the model. • Definitions of variables. • Explanation of the different parts of the model and how they relate to each other. • Justification of the model and its parts. 3 (5) Mathematical Analysis: Must include: • Qualitative Analysis: Discuss what mathematical information the qualitative analysis gives about the solution. • Analytical Analysis: Solve and discuss what mathematical information the analytical analysis gives about the solution. (6) Prediction, Interpretation, and Evaluation: Must include: • Prediction: Make predictions based on the model. See the project directions. • Interpretations: Be sure to state what your solution and predictions mean or say in terms of the applied problem. This should be done throughout the write-up as necessary. • Evaluation: Critique the interpretations and predictions. Do the interpretations of the solution and predictions make sense for that applied problem? Why or why not? • Evaluation: What might your solutions and predictions imply and why is it important for the people, animals, or objects in the applied problem? Does it imply any actions that should be taken in the future, i.e. do you have any recommendations based on your conclusion?
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Running Head: MATHEMATICAL MODEL

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Mathematical Model
Institutional Affiliations
Date

MATHEMATICAL MODEL

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1. Problem Introduction
Considering the tuition and fees rising to about 5.4% higher than the rate of inflation,
college fee payment is an escalating cost for most parents (College Scholarships, 2018). In such
cases, the easiest and cheapest way to finance a college education is through grants and
scholarships which do not require repayments. However, the next viable option involves
dependence on personal income and savings. For example, parents can decide to create college
savings account even as early as after a child is born. Such saving accounts are the most reliable
and can guarantee full fee payment if well modeled.
Basic requirements for a successful savings account is a clear understanding of the cash
flow. For instance, knowing how much a person spends and the amount of income ensures a
strong plan of awareness. A parent should first consider the monthly income, the amount already
in savings and then subtract the amount from the expected and recurring expenses throughout the
school year. However, due to the limited scope of this paper, we will consider some, but not all
of the variables involved in child expenditure while at school (See the assumptions section).
Hence, this paper aims to create a mathematical model on what the approach to completely pay
for a child’s college education. It begins with basic assumptions of the model and building on the
components of the model. Later, an actual analysis, summary, and sensitivity analysis of the
model will be addressed.
1.1. Assumptions of the model
As stated in the introduction section, some variables will not be considered in the
development of this model. Nevertheless, some will be abstractly included in the equation. For
example, student expenditure on food, travel, and other arising requirements may ...


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