In the early days of AIDS, the growth factor was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If this had continued unchecked, how many people would have died from AIDS in 2003?

Question

Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?

Answer 1

The basic exponential growth function is:

f(t) = a·b^t

1. f (t) = number of cases at year t
2. a = starting value = 1800 in 1983
3. b = growth factor = 1.8
4. t = years since 1983 = 2003 - 1983 = 20

f(t) = 1800·(1.8)²⁰

Use your calculator to compute the answer.