Mathematical Modeling Task 2

A. Examine the five models in the “Data and Graphs” attachment by doing the following:
1. Compare the five models based on their graphical qualities.
2. Compare the five models based on their R2 values.
3. Explain which model is the most accurate based on the comparisons in part A1 and A2.
Note: R2 is the square of the correlation coefficient between the data and the model.
B. Given that the actual U.S. population in 2010 was 308.75 million, explain which of the following models is the most accurate. Base your explanation only on the following U.S. population predictions (in millions) by each model, including computations of the percent errors, for the year 2010:
• linear: 242.89
• exponential: 515.34
• quadratic: 304.36
• third-degree polynomial: 308.22
• fourth-degree polynomial: 311.96
Note: Percent error is defined as the following: Percent error =( |estimate−actual|/actual )x 100.
C. Justify which model is the most accurate by comparing your results of methods used in parts A and B.
D. Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.