GROUP PROJECT : Types of modeling functions Group …



FINAL MODELING PROJECT

In this project we will investigate the best fit model for three sets of data. You need to include all your work; I will give no credit for answers only. All scatter plots and graphs should be on graph paper or created on Excel. You need to show all the data points in the set and label all other relevant points ( ex: max, min, intercepts etc.)

Here are the data sets for the project:

Data Set 1: Percent of U.S. Population without health care. (Source: US Bureau of Census)

| |

|Percent of U.S. Population without Health Care |

| Year |

| Year | 1992 |

| |t = 1 |

|1983 |23,646 |

|1984 |23,758 |

|1985 |22,716 |

|1986 |24,045 |

|1987 |23,641 |

|1988 |23,646 |

|1989 |22,404 |

|1990 |22,084 |

|1991 |19,887 |

|1992 |17,858 |

|1993 |17,474 |

|1994 |16,580 |

|1995 |17,247 |

|1996 |17,218 |

|1997 |16,485 |

|1998 |16,020 |

|1999 |15,786 |

Please do the following for each the data set:

1) Use common differences to determine what type of function best models the data: constant, linear, quadratic, cubic, quartic, or exponential growth or decay. Give reasons to support your choice of function. Be sure to show your calculations (neatly please!).

2) Sketch a scatter plot for each data set. Be sure to label your axes and indicate your scale.

(It may be helpful to use a graphing calculator).

3) Find the best fit model (function) for each data set. You may use the regression feature of your calculator.

4) Make a graph containing both the scatter plot and the modeling function. (A graphing calculator would be helpful). Does the graph fit most of the data points? Compare this graph with your scatter plot from part

(2). What observations do you have ?

(Hint: Both the graph and the scatter plot should be on the same window screen on your

graphing calculator for easier comparison).

5) For each data set, comment on the following:

a) Does the modeling function and its graph show certain trend ( increasing, decreasing,

constant, exponentially growth, exponentially decay etc ) ?

b) Is the rate of change constant, a constant percent, or something else?

c) Describe the end behavior of the graph of the function as [pic] and as [pic].

6) Find the x-intercept(s), y – intercept, max/min points, if they exist, then interpret these in the

context of the data. Remember to locate and label these relevant points on your graph.

b) What do the domain and range of your model appear to be?

(Express your answers in interval notations).

(Hint: Use your graph to help you. Is the data set included in the domain and range of your model?)

7) Find the initial value of your model, then interpret it in the context of the data.

8) Find the domain and range for your model, both from a purely mathematical standpoint and also in

the context of the problem. Are they the same? Does this make sense? Explain.

9) Choose an input value NOT in the data set and make a prediction about the output.

a) Choose an input value between two of the given data values.

b) Choose an input greater than the largest given data value.

Do you think your model is an accurate predictor for these values? Please generalize a bit: For what

input values is your model a good predictor of the outputs? For what input values is it not so good?

I will use the following rubric when grading your project. Remember, this project is worth 50 points. You need to be clear, concise, detailed, and neat.

Enjoy!

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