Chapter 2
Models of Growth: Rates of Change
Project 1: The Early Spread of AIDS in the US
- Introduction
- Plotting the Data
- Finding a Model Function
- Checking Your Model Function
- Using Your Model Function
Plotting the Data
The following table* describes the early spread of the AIDS epidemic in the U.S. by showing the total numbers of AIDS cases reported to the Centers for Disease Control as of the indicated dates.
| Month | Months
from Jan 1, 1980 |
Number
of Cases |
Month | Months
from Jan 1, 1980 |
Number
of Cases |
|
| Sep 1981 | 20 |
110 |
Dec 1984 | 59 |
7,025 |
|
| Oct 1981 | 21 |
129 |
Mar 1985 | 62 |
8,229 |
|
| Jan 1982 | 24 |
220 |
Aug 1985 | 67 |
12,067 |
|
| Mar 1982 | 26 |
257 |
Oct 1985 | 69 |
14,049 |
|
| Jun 1982 | 29 |
439 |
Feb 1986 | 73 |
16,458 |
|
| Aug 1982 | 31 |
514 |
Dec 1986 | 83 |
28,098 |
|
| Dec 1982 | 35 |
878 |
Jun 1987 | 89 |
36,058 |
|
| Feb 1983 | 37 |
1,029 |
Mar 1988 | 98 |
56,575 |
|
| Jun 1983 | 41 |
1,756 |
Dec 1989 | 119 |
113,891 |
|
| Sep 1983 | 44 |
2,057 |
Dec 1991 | 143 |
202,843 |
|
| Feb 1984 | 49 |
3,512 |
Aug 1992 | 151 |
226,252 |
|
| May 1984 | 52 |
4,115 |
You will find in your worksheet a set of commands for plotting the list of data points. Enter these commands now.
Change the plot to a semilog plot, and describe what you see. What would it mean if the data points line up roughly along a straight line? Is that the case here? What do you conclude?
Now change the plot to a log-log plot, and describe what you see. What would it mean if the data points line up roughly along a straight line? Is that the case here? What do you conclude?
In the next part you will use your observation about the type of growth to find a formula for the number of cases as a function of time.
* Derived from the Morbidity and Mortality Weekly Report of the Centers for Disease Control.
