Math 125 Pre-Calculus Spring 2014 K

Math 125 Pre Calculusname Spring 2014 K

In this assignment, students are tasked with solving a variety of mathematical problems related to percentages, exponential functions, population models, interest rates, and graph analysis. The problems require applying knowledge of decay, growth models, algebra, and exponential functions to real-world scenarios including investments, pharmaceuticals, population changes, and banking interest calculations.

Paper For Above instruction

The assignment covers a broad spectrum of fundamental concepts in pre-calculus, emphasizing applications of exponential decay and growth, percentage calculations, and interpretations of mathematical functions within real-world contexts. These topics are essential for developing quantitative reasoning skills applicable in finance, biology, and social sciences.

Problem 1 involves calculating the total percentage decrease of an investment that depreciates by 5% annually over four years. This problem emphasizes understanding compound percentage decrease and the concept of exponential decay. The solution requires recognizing that successive decreases compound multiplicatively rather than additively, leading to the formula for the remaining amount after four years and calculating the total percentage loss.

The second problem focuses on pharmacokinetics, where the amount of a drug in the body is modeled by an exponential decay function of time. The specific questions explore initial dose, rate of drug elimination, remaining drug after a specific period, and the drug’s half-life. These calculations highlight the application of exponential decay functions to biological processes, demonstrating how to interpret parameters within the model and solve for unknowns based on the function’s properties.

Problem 3 extends the concept to population dynamics, requiring the formulation of models based on constant decline in population either by a fixed number or a percentage. This strengthens understanding of linear versus exponential models and how to write equations based on initial conditions and growth/decay rates, illustrating real-world demographic changes.

Problem 4 asks for constructing an exponential function based on given data features, which involves utilizing points on a graph and applying the exponential growth/decay formula to derive the function’s parameters. This helps develop skills in function modeling from empirical data.

Problem 5 involves comparing different exponential functions to determine which has the largest or smallest values for given parameters. This promotes understanding of how parameters a and b influence the behavior of exponential functions and fosters analytical reasoning about function characteristics.

Problem 6 requires estimation based on a graph, which develops skills in interpreting and analyzing graphical data visually, crucial for real-world data analysis and interpretation.

Problems 7 and 8 focus on financial mathematics, specifically calculating effective annual interest rates and future balances with different compounding frequencies. These tasks highlight the importance of understanding nominal versus effective rates and their implications for investment and savings decisions, reinforcing financial literacy skills.

In sum, this assignment integrates multiple aspects of pre-calculus with practical applications, encouraging students to connect theoretical concepts with real-world scenarios involving decay, growth, and financial calculations. Developing proficiency in these areas enhances both mathematical reasoning and practical decision-making skills across various disciplines.

References

• Anton, H., Bivens, L., & Davis, S. (2019). Basic College Mathematics (12th ed.). Wiley.
• Blitzer, R. (2018). Algebra and Trigonometry. Pearson.
• Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
• Hill, T. P. (2017). Mathematics for Business and Social Sciences. McGraw-Hill Education.
• Larson, R., & Hostetler, R. P. (2018). Precalculus with Limits: A Graphing Approach. Cengage Learning.
• Swokla, M., & Bittinger, M. (2019). Precalculus: Graphical, Numerical, algebraic. Pearson.
• Stewart, J., Redlin, L., & Watson, S. (2018). Precalculus. Cengage Learning.
• Thomas, G. B., & Finney, R. L. (2018). Calculus and Analytic Geometry. Pearson.
• Yates, S. J. (2020). Mathematical Methods for Business and Finance. Routledge.
• Wagner, C. (2017). Financial Mathematics: A Study Guide. Springer.