Answer:
To use the exponential growth model to estimate the number of people who would have died from AIDS in 2003, we need to know the initial value (the starting point) and the growth factor.
Step-by-step explanation: From the problem statement, we know that the growth factor in the early days of AIDS was around 2.2. This means that the number of AIDS deaths would roughly double every year.
In 1983, about 1600 people in the U.S. died of AIDS. This is our initial value.
To estimate the number of people who would have died from AIDS in 2003, we need to know how many years have passed since 1983.
2003 - 1983 = 20 years
So we need to apply the growth factor 20 times to the initial value of 1600.
Using the formula for exponential growth:
y = a * r^t
where y is the final value, a is the initial value, r is the growth factor, and t is the number of periods (in this case, years).
y = 1600 * (2.2)^20
y = 1600 * 47516.45
y = 76,026,320
Therefore, if the trend of AIDS deaths had continued unchecked with a growth factor of 2.2, it is estimated that about 76 million people in the U.S. would have died from AIDS by 2003. It's important to note that this is a theoretical estimate based on the assumption of exponential growth, and many factors could have affected the actual number of AIDS deaths over time.