Guidelines: You should consider your project as a technical paper (like an English paper only different). Part of your grade will be based on the quality of your written presentation. The paper you turn in should have a mix of equations, formulas and prose. Graphs may be copied directly from your calculator, but should be clearly labelled. Use complete sentences, good grammar and correct punctuation. Spelling is also important. You should aim to write your report in such a way that it can be read and understood by anyone who knows the material for this course.
Use the data from Table I to find a formula which approximately models the growth of the population over the years 1790-1850. You'll have to consider what {\it sort} of function might describe this growth. Justify your choice of model and comment on how well it fits the data. [You might want to discuss such points as: how accurate the model is over the range 1790-1850; how accurate the model is over the range 1790-1990; the factors which contribute to the discrepancy between the model and the data; and the prediction your model gives for the current US population.]
Year | Population | Year | Population |
1790 | 3.9 | 1800 | 5.3 |
1810 | 7.2 | 1820 | 9.6 |
1830 | 12.9 | 1840 | 17.1 |
1850 | 23.1 |
TABLE I: US population (in millions), 1790--1850
1860 | 31.4 | 1930 | 122.8 |
1870 | 38.6 | 1940 | 131.7 |
1880 | 50.2 | 1950 | 150.7 |
1890 | 62.9 | 1960 | 179.0 |
1900 | 76.0 | 1970 | 205.0 |
1910 | 92.0 | 1980 | 226.5 |
1920 | 105.7 | 1990 | 248.7 |
TABLE II: US population (in millions), 1860--1990
Year | 1900 | 1910 | 1920 | 1930 | 1940 |
Vehicles | 8 | 458.3 | 8131.5 | 23035 | 27466 |
Year | 1950 | 1960 | 1970 | 1980 | 1990 |
Vehicles | 40339 | 61682 | 89279 | 121601 | 143550 |
TABLE III Automobile registration in the US (in thousands) 1900--1990
Use the data from Table II to estimate, to within 1 year, the first year when there was at least one car for every two Americans. You should include a plot of the data in Table III. Try to find the answer both graphically and analytically. Discuss the strengths and weaknesses of the model for automobile registration you used.
The TI can plot tabular data if you tell it a list of x-coordinates and a list of y-coordinates. Bring up the STAT menu. Press CALC and you'll be asked to give the names of your two lists. Probably you want the years to be your x-coordinates and the other data to be your y-coordinates. Once you enter the names you can EXIT back to the STAT menu. The menu item DRAW allows you to plot your data points.
Warnings: The TI plots not only your data but also any currently selected graphing functions. The viewing window is set using GRAPH: RANGE just as it would be for a graph.) You have two options for plotting your data: SCAT just plots the points, xyLINE plots the points and joins consecutive ones with straight lines.
Notes: