To calculate the number of people who would have died from AIDS in 2006 using the exponential growth model, we need to find the growth factor (common ratio) per year and then apply it repeatedly to project the number of deaths.
Given information:
Growth factor (common ratio) = 2.0
Number of deaths in 1983 = 1900
Let's calculate the number of deaths for each year until 2006:
From 1983 to 2006, there are 23 years in total (2006 - 1983 = 23).
We can use the exponential growth formula to calculate the number of deaths for each year:
Number of deaths (t) = Initial number of deaths * Growth factor^t
where t represents the number of years after the initial year (1983 in this case).
Calculate the number of deaths for each year:
Number of deaths (1983) = 1900 (given)
Number of deaths (1984) = 1900 * 2.0^1 = 1900 * 2 = 3800
Number of deaths (1985) = 1900 * 2.0^2 = 1900 * 4 = 7600
Number of deaths (1986) = 1900 * 2.0^3 = 1900 * 8 = 15200
And so on, until 2006:
Number of deaths (2006) = 1900 * 2.0^23 ≈ 1900 * 8,388,608 ≈ 15,937,655,200
Therefore, if the trend had continued unchecked, around 15,937,655,200 people would have died from AIDS in the U.S. in 2006. Please note that this projection is purely based on the exponential growth model and assumes no intervention or changes in the trend over time, which may not reflect the actual number of deaths.